7*x^3-50*x+7=0

$$7 x^{3} – 50 x + 7 = 0$$

/ 1 / / 1
50*re|——————————————–| | 50*im|——————————————–| / / __________ / / __________| / / __________ / / __________
| _______________________| | | _______________________| | |/ 10305519 || | |/ 10305519 ||| | |/ 10305519 || | |/ 10305519 ||
|/ ___ / __________ | | |/ ___ / __________ | |atan|————|| |atan|————||| |atan|————|| |atan|————||
|| 1 I*/ 3 | / 27 3*I*/ 10305519 | | || 1 I*/ 3 | / 27 3*I*/ 10305519 | ____ | 441 /| ____ | 441 /|| ____ | 441 /| ____ | 441 /|
||- – – ——-|*3 / — + —————- | | ||- – – ——-|*3 / — + —————- | 5*/ 14 *cos|——————| 5*/ 42 *sin|——————|| 5*/ 14 *sin|——————| 5*/ 42 *cos|——————|
2 2 / / 2 98 / | 2 2 / / 2 98 / 3 / 3 /| 3 / 3 /
x1 = – ————————————————— + I*|- ————————————————— + ——————————– + ——————————–| – ——————————– + ——————————–
7 7 14 42 / 14 42

$$x_{1} = – frac{5 sqrt{14}}{14} sin{left (frac{1}{3} {atan}{left (frac{sqrt{10305519}}{441} right )} right )} – frac{50}{7} Re{left(frac{1}{left(- frac{1}{2} – frac{sqrt{3} i}{2}right) sqrt[3]{frac{27}{2} + frac{3 i}{98} sqrt{10305519}}}right)} + frac{5 sqrt{42}}{42} cos{left (frac{1}{3} {atan}{left (frac{sqrt{10305519}}{441} right )} right )} + i left(- frac{50}{7} Im{left(frac{1}{left(- frac{1}{2} – frac{sqrt{3} i}{2}right) sqrt[3]{frac{27}{2} + frac{3 i}{98} sqrt{10305519}}}right)} + frac{5 sqrt{42}}{42} sin{left (frac{1}{3} {atan}{left (frac{sqrt{10305519}}{441} right )} right )} + frac{5 sqrt{14}}{14} cos{left (frac{1}{3} {atan}{left (frac{sqrt{10305519}}{441} right )} right )}right)$$

/ 1 / / 1
50*re|——————————————–| | 50*im|——————————————–| / / __________ / / __________| / / __________ / / __________
| _______________________| | | _______________________| | |/ 10305519 || | |/ 10305519 ||| | |/ 10305519 || | |/ 10305519 ||
|/ ___ / __________ | | |/ ___ / __________ | |atan|————|| |atan|————||| |atan|————|| |atan|————||
|| 1 I*/ 3 | / 27 3*I*/ 10305519 | | || 1 I*/ 3 | / 27 3*I*/ 10305519 | ____ | 441 /| ____ | 441 /|| ____ | 441 /| ____ | 441 /|
||- – + ——-|*3 / — + —————- | | ||- – + ——-|*3 / — + —————- | 5*/ 14 *cos|——————| 5*/ 42 *sin|——————|| 5*/ 14 *sin|——————| 5*/ 42 *cos|——————|
2 2 / / 2 98 / | 2 2 / / 2 98 / 3 / 3 /| 3 / 3 /
x2 = – ————————————————— + I*|- ————————————————— – ——————————– + ——————————–| + ——————————– + ——————————–
7 7 14 42 / 14 42

$$x_{2} = frac{5 sqrt{14}}{14} sin{left (frac{1}{3} {atan}{left (frac{sqrt{10305519}}{441} right )} right )} + frac{5 sqrt{42}}{42} cos{left (frac{1}{3} {atan}{left (frac{sqrt{10305519}}{441} right )} right )} – frac{50}{7} Re{left(frac{1}{left(- frac{1}{2} + frac{sqrt{3} i}{2}right) sqrt[3]{frac{27}{2} + frac{3 i}{98} sqrt{10305519}}}right)} + i left(- frac{5 sqrt{14}}{14} cos{left (frac{1}{3} {atan}{left (frac{sqrt{10305519}}{441} right )} right )} + frac{5 sqrt{42}}{42} sin{left (frac{1}{3} {atan}{left (frac{sqrt{10305519}}{441} right )} right )} – frac{50}{7} Im{left(frac{1}{left(- frac{1}{2} + frac{sqrt{3} i}{2}right) sqrt[3]{frac{27}{2} + frac{3 i}{98} sqrt{10305519}}}right)}right)$$

_______________________
/ __________
/ 27 3*I*/ 10305519
3 / — + —————-
50 / 2 98
x3 = – —————————— – —————————-
_______________________ 3
/ __________
/ 27 3*I*/ 10305519
7*3 / — + —————-
/ 2 98

$$x_{3} = – frac{1}{3} sqrt[3]{frac{27}{2} + frac{3 i}{98} sqrt{10305519}} – frac{50}{7 sqrt[3]{frac{27}{2} + frac{3 i}{98} sqrt{10305519}}}$$

x1 = 2.59965195070000

x2 = 0.140387357558000

x3 = -2.74003930826000