Solve x^3-41x-20=0

$${ x }^{ 3 } -41x-20=0$$

Solve for x (complex solution)

$$x=-\frac{3^{\frac{5}{6}}\left(1+\sqrt{3}i\right)\left(90+\sqrt{198663}i\right)^{-\frac{1}{3}}\left(\left(-\sqrt{3}-3i\right)\left(90+\sqrt{198663}i\right)^{\frac{2}{3}}+82\times 3^{\frac{5}{6}}\right)}{36}\approx -6.143664535-3.947459643 \cdot 10^{-16}i$$

$$x=\frac{3^{\frac{2}{3}}\left(90+\sqrt{198663}i\right)^{-\frac{1}{3}}\left(\left(3\left(90+\sqrt{198663}i\right)\right)^{\frac{2}{3}}+123\right)}{9}\approx 6.634350978-7.894919286 \cdot 10^{-16}i$$

$$x=-\frac{3^{\frac{5}{6}}\left(90+\sqrt{198663}i\right)^{-\frac{1}{3}}\left(-\sqrt{3}i+1\right)\left(\left(-\sqrt{3}+3i\right)\left(90+\sqrt{198663}i\right)^{\frac{2}{3}}+82\times 3^{\frac{5}{6}}\right)}{36}\approx -0.490686442+9.560253823 \cdot 10^{-16}i$$

Solve for x

$$x=-\frac{\sqrt{123}\left(\sqrt{3}\sin(\frac{\arccos(\frac{30\sqrt{123}}{1681})}{3})+\cos(\frac{\arccos(\frac{30\sqrt{123}}{1681})}{3})\right)}{3}\approx -6.143664535$$

$$x=\frac{2\sqrt{123}\cos(\frac{\arccos(\frac{30\sqrt{123}}{1681})}{3})}{3}\approx 6.634350978$$

$$x=\frac{\sqrt{123}\left(\sqrt{3}\sin(\frac{\arccos(\frac{30\sqrt{123}}{1681})}{3})-\cos(\frac{\arccos(\frac{30\sqrt{123}}{1681})}{3})\right)}{3}\approx -0.490686442$$