x^3+6*x^2+9*x+8=0

$$9 x + x^{3} + 6 x^{2} + 8 = 0$$

_______________ / _______________
3 / ___ | ___ ___ 3 / ___ |
/ 81 + 54*/ 2 3 | 3*/ 3 / 3 */ 81 + 54*/ 2 |
x1 = -2 + —————— + ——————– + I*|- ——————– + ————————|
6 _______________ | _______________ 6 |
3 / ___ | 3 / ___ |
2*/ 81 + 54*/ 2 2*/ 81 + 54*/ 2 /

$$x_{1} = -2 + frac{3}{2 sqrt[3]{54 sqrt{2} + 81}} + frac{1}{6} sqrt[3]{54 sqrt{2} + 81} + i left(- frac{3 sqrt{3}}{2 sqrt[3]{54 sqrt{2} + 81}} + frac{sqrt{3}}{6} sqrt[3]{54 sqrt{2} + 81}right)$$

_______________ / _______________
3 / ___ | ___ 3 / ___ ___ |
/ 81 + 54*/ 2 3 | / 3 */ 81 + 54*/ 2 3*/ 3 |
x2 = -2 + —————— + ——————– + I*|- ———————— + ——————–|
6 _______________ | 6 _______________|
3 / ___ | 3 / ___ |
2*/ 81 + 54*/ 2 2*/ 81 + 54*/ 2 /

$$x_{2} = -2 + frac{3}{2 sqrt[3]{54 sqrt{2} + 81}} + frac{1}{6} sqrt[3]{54 sqrt{2} + 81} + i left(- frac{sqrt{3}}{6} sqrt[3]{54 sqrt{2} + 81} + frac{3 sqrt{3}}{2 sqrt[3]{54 sqrt{2} + 81}}right)$$

_______________
3 / ___
3 / 81 + 54*/ 2
x3 = -2 – —————— – ——————
_______________ 3
3 / ___
/ 81 + 54*/ 2

$$x_{3} = -2 – frac{1}{3} sqrt[3]{54 sqrt{2} + 81} – frac{3}{sqrt[3]{54 sqrt{2} + 81}}$$

x1 = -0.822349301196 + 1.07730381285*i

x2 = -0.822349301196 – 1.07730381285*i

x3 = -4.35530139761000