x^2+3*y=31 2*x^2+6*y^2=31*x

$$x^{2} + 3 y = 31$$

2 2
2*x + 6*y = 31*x

$$2 x^{2} + 6 y^{2} = 31 x$$

$$x_{1} = – frac{3}{31} sqrt{- frac{140815}{324 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}}} – frac{121}{9} + 2 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}}} + frac{59}{31} + frac{6}{31} left(frac{1}{2} + frac{1}{2} sqrt{- frac{140815}{324 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}}} – frac{121}{9} + 2 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}}} – frac{1}{2} sqrt{- frac{961}{6 sqrt{- frac{140815}{324 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}}} – frac{121}{9} + 2 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}}}} – 2 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}} – frac{242}{9} + frac{140815}{324 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}}}}right)^{2} + frac{3}{31} sqrt{- frac{961}{6 sqrt{- frac{140815}{324 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}}} – frac{121}{9} + 2 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}}}} – 2 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}} – frac{242}{9} + frac{140815}{324 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}}}}$$
=
$$- frac{3}{31} sqrt{- frac{140815}{324 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}}} – frac{121}{9} + 2 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}}} + frac{59}{31} + frac{6}{31} left(frac{1}{2} + frac{1}{2} sqrt{- frac{140815}{324 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}}} – frac{121}{9} + 2 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}}} – frac{i}{2} sqrt{- frac{140815}{324 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}}} + frac{242}{9} + 2 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}} + frac{961}{6 sqrt{- frac{140815}{324 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}}} – frac{121}{9} + 2 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}}}}}right)^{2} + frac{3 i}{31} sqrt{- frac{140815}{324 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}}} + frac{242}{9} + 2 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}} + frac{961}{6 sqrt{- frac{140815}{324 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}}} – frac{121}{9} + 2 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}}}}}$$
=

-5.50326661713784 – 1.70244683183435*i

$$y_{1} = frac{1}{2} + frac{1}{2} sqrt{- frac{140815}{324 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}}} – frac{121}{9} + 2 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}}} – frac{1}{2} sqrt{- frac{961}{6 sqrt{- frac{140815}{324 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}}} – frac{121}{9} + 2 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}}}} – 2 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}} – frac{242}{9} + frac{140815}{324 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}}}}$$
=
$$frac{1}{2} + frac{1}{2} sqrt{- frac{140815}{324 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}}} – frac{121}{9} + 2 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}}} – frac{i}{2} sqrt{- frac{140815}{324 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}}} + frac{242}{9} + 2 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}} + frac{961}{6 sqrt{- frac{140815}{324 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}}} – frac{121}{9} + 2 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}}}}}$$
=

1.204127251973 – 6.24601254472403*i

$$x_{2} = – frac{3}{31} sqrt{- frac{140815}{324 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}}} – frac{121}{9} + 2 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}}} + frac{59}{31} – frac{3}{31} sqrt{- frac{961}{6 sqrt{- frac{140815}{324 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}}} – frac{121}{9} + 2 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}}}} – 2 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}} – frac{242}{9} + frac{140815}{324 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}}}} + frac{6}{31} left(frac{1}{2} + frac{1}{2} sqrt{- frac{140815}{324 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}}} – frac{121}{9} + 2 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}}} + frac{1}{2} sqrt{- frac{961}{6 sqrt{- frac{140815}{324 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}}} – frac{121}{9} + 2 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}}}} – 2 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}} – frac{242}{9} + frac{140815}{324 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}}}}right)^{2}$$
=
$$- frac{3}{31} sqrt{- frac{140815}{324 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}}} – frac{121}{9} + 2 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}}} + frac{59}{31} – frac{3 i}{31} sqrt{- frac{140815}{324 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}}} + frac{242}{9} + 2 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}} + frac{961}{6 sqrt{- frac{140815}{324 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}}} – frac{121}{9} + 2 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}}}}} + frac{6}{31} left(frac{1}{2} + frac{1}{2} sqrt{- frac{140815}{324 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}}} – frac{121}{9} + 2 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}}} + frac{i}{2} sqrt{- frac{140815}{324 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}}} + frac{242}{9} + 2 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}} + frac{961}{6 sqrt{- frac{140815}{324 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}}} – frac{121}{9} + 2 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}}}}}right)^{2}$$
=

-5.50326661713784 + 1.70244683183435*i

$$y_{2} = frac{1}{2} + frac{1}{2} sqrt{- frac{140815}{324 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}}} – frac{121}{9} + 2 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}}} + frac{1}{2} sqrt{- frac{961}{6 sqrt{- frac{140815}{324 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}}} – frac{121}{9} + 2 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}}}} – 2 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}} – frac{242}{9} + frac{140815}{324 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}}}}$$
=
$$frac{1}{2} + frac{1}{2} sqrt{- frac{140815}{324 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}}} – frac{121}{9} + 2 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}}} + frac{i}{2} sqrt{- frac{140815}{324 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}}} + frac{242}{9} + 2 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}} + frac{961}{6 sqrt{- frac{140815}{324 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}}} – frac{121}{9} + 2 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}}}}}$$
=

1.204127251973 + 6.24601254472403*i

$$x_{3} = frac{3}{31} sqrt{- frac{140815}{324 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}}} – frac{121}{9} + 2 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}}} + frac{3}{31} sqrt{- 2 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}} – frac{242}{9} + frac{140815}{324 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}}} + frac{961}{6 sqrt{- frac{140815}{324 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}}} – frac{121}{9} + 2 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}}}}} + frac{59}{31} + frac{6}{31} left(- frac{1}{2} sqrt{- 2 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}} – frac{242}{9} + frac{140815}{324 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}}} + frac{961}{6 sqrt{- frac{140815}{324 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}}} – frac{121}{9} + 2 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}}}}} – frac{1}{2} sqrt{- frac{140815}{324 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}}} – frac{121}{9} + 2 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}}} + frac{1}{2}right)^{2}$$
=
$$frac{3}{31} sqrt{- frac{140815}{324 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}}} – frac{121}{9} + 2 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}}} + frac{3}{31} sqrt{- 2 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}} – frac{242}{9} + frac{140815}{324 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}}} + frac{961}{6 sqrt{- frac{140815}{324 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}}} – frac{121}{9} + 2 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}}}}} + frac{59}{31} + frac{6}{31} left(- frac{1}{2} + frac{1}{2} sqrt{- frac{140815}{324 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}}} – frac{121}{9} + 2 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}}} + frac{1}{2} sqrt{- 2 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}} – frac{242}{9} + frac{140815}{324 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}}} + frac{961}{6 sqrt{- frac{140815}{324 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}}} – frac{121}{9} + 2 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}}}}}right)^{2}$$
=

6.65497764713416

$$y_{3} = – frac{1}{2} sqrt{- 2 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}} – frac{242}{9} + frac{140815}{324 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}}} + frac{961}{6 sqrt{- frac{140815}{324 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}}} – frac{121}{9} + 2 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}}}}} – frac{1}{2} sqrt{- frac{140815}{324 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}}} – frac{121}{9} + 2 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}}} + frac{1}{2}$$
=
$$- frac{1}{2} sqrt{- 2 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}} – frac{242}{9} + frac{140815}{324 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}}} + frac{961}{6 sqrt{- frac{140815}{324 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}}} – frac{121}{9} + 2 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}}}}} – frac{1}{2} sqrt{- frac{140815}{324 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}}} – frac{121}{9} + 2 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}}} + frac{1}{2}$$
=

-4.42957582795178

$$x_{4} = – frac{3}{31} sqrt{- 2 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}} – frac{242}{9} + frac{140815}{324 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}}} + frac{961}{6 sqrt{- frac{140815}{324 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}}} – frac{121}{9} + 2 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}}}}} + frac{3}{31} sqrt{- frac{140815}{324 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}}} – frac{121}{9} + 2 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}}} + frac{59}{31} + frac{6}{31} left(- frac{1}{2} sqrt{- frac{140815}{324 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}}} – frac{121}{9} + 2 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}}} + frac{1}{2} + frac{1}{2} sqrt{- 2 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}} – frac{242}{9} + frac{140815}{324 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}}} + frac{961}{6 sqrt{- frac{140815}{324 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}}} – frac{121}{9} + 2 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}}}}}right)^{2}$$
=
$$- frac{3}{31} sqrt{- 2 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}} – frac{242}{9} + frac{140815}{324 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}}} + frac{961}{6 sqrt{- frac{140815}{324 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}}} – frac{121}{9} + 2 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}}}}} + frac{3}{31} sqrt{- frac{140815}{324 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}}} – frac{121}{9} + 2 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}}} + frac{59}{31} + frac{6}{31} left(- frac{1}{2} sqrt{- frac{140815}{324 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}}} – frac{121}{9} + 2 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}}} + frac{1}{2} + frac{1}{2} sqrt{- 2 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}} – frac{242}{9} + frac{140815}{324 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}}} + frac{961}{6 sqrt{- frac{140815}{324 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}}} – frac{121}{9} + 2 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}}}}}right)^{2}$$
=

4.35155558714153

$$y_{4} = – frac{1}{2} sqrt{- frac{140815}{324 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}}} – frac{121}{9} + 2 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}}} + frac{1}{2} + frac{1}{2} sqrt{- 2 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}} – frac{242}{9} + frac{140815}{324 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}}} + frac{961}{6 sqrt{- frac{140815}{324 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}}} – frac{121}{9} + 2 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}}}}}$$
=
$$- frac{1}{2} sqrt{- frac{140815}{324 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}}} – frac{121}{9} + 2 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}}} + frac{1}{2} + frac{1}{2} sqrt{- 2 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}} – frac{242}{9} + frac{140815}{324 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}}} + frac{961}{6 sqrt{- frac{140815}{324 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}}} – frac{121}{9} + 2 sqrt[3]{frac{512076937}{186624} + frac{29791 sqrt{8619329}}{20736}}}}}$$
=

4.02132132400579

x1 = 4.351555587141526
y1 = 4.021321324005789