Solve x^3+10x^2-15x-6=0

$$x ^ { 3 } + 10 x ^ { 2 } - 15 x - 6 = 0$$

Solve for x (complex solution)

$$x=\frac{\sqrt{3}i\sqrt[3]{-1594+9\sqrt{6269}i}}{6}-\frac{145\sqrt{3}i\left(-1594+9\sqrt{6269}i\right)^{-\frac{1}{3}}}{6}-\frac{\sqrt[3]{-1594+9\sqrt{6269}i}}{6}-\frac{145\left(-1594+9\sqrt{6269}i\right)^{-\frac{1}{3}}}{6}-\frac{10}{3}\approx -11.282371919-6.661338148 \cdot 10^{-16}i$$

$$x=\frac{\sqrt[3]{-1594+9\sqrt{6269}i}+145\left(-1594+9\sqrt{6269}i\right)^{-\frac{1}{3}}-10}{3}\approx 1.612227927-1.184237893 \cdot 10^{-15}i$$

$$x=-\frac{\sqrt{3}i\sqrt[3]{-1594+9\sqrt{6269}i}}{6}+\frac{145\sqrt{3}i\left(-1594+9\sqrt{6269}i\right)^{-\frac{1}{3}}}{6}-\frac{\sqrt[3]{-1594+9\sqrt{6269}i}}{6}-\frac{145\left(-1594+9\sqrt{6269}i\right)^{-\frac{1}{3}}}{6}-\frac{10}{3}\approx -0.329856008+1.998401444 \cdot 10^{-15}i$$

Solve for x

$$x=\frac{2\left(-\sqrt{145}\cos(\frac{\arccos(\frac{1594\sqrt{145}}{21025})}{3})-5\right)}{3}\approx -11.282371919$$

$$x=\frac{\sqrt{145}\left(\sqrt{3}\sin(\frac{\arccos(\frac{1594\sqrt{145}}{21025})}{3})+\cos(\frac{\arccos(\frac{1594\sqrt{145}}{21025})}{3})\right)-10}{3}\approx 1.612227927$$

$$x=\frac{\sqrt{145}\left(-\sqrt{3}\sin(\frac{\arccos(\frac{1594\sqrt{145}}{21025})}{3})+\cos(\frac{\arccos(\frac{1594\sqrt{145}}{21025})}{3})\right)-10}{3}\approx -0.329856008$$