Solve 0.038408*x^3=3x+1

$$0.038408 \times { x }^{ 3 } =3x+1$$

Solve for x (complex solution)

$$x=-\frac{25\times 92198404^{\frac{2}{3}}\left(1+i\sqrt{3}\right)\left(4801+i\sqrt{2377450399}\right)^{-\frac{1}{3}}\left(4801\times \left(4\left(4801+i\sqrt{2377450399}\right)\right)^{\frac{2}{3}}\left(-i\sqrt{3}-1\right)+400\times 23049601^{\frac{2}{3}}\right)}{1770578150416}\approx -8.666280144$$

$$x=\frac{25\times 92198404^{\frac{2}{3}}\left(4801+i\sqrt{2377450399}\right)^{-\frac{1}{3}}\left(4801\times \left(4\left(4801+i\sqrt{2377450399}\right)\right)^{\frac{2}{3}}+200\times 23049601^{\frac{2}{3}}\right)}{442644537604}\approx 9.000089686+1.103100137 \cdot 10^{-15}i$$

$$x=-\frac{25\times 92198404^{\frac{2}{3}}\left(4801+i\sqrt{2377450399}\right)^{-\frac{1}{3}}\left(-i\sqrt{3}+1\right)\left(4801\left(-1+i\sqrt{3}\right)\times \left(4\left(4801+i\sqrt{2377450399}\right)\right)^{\frac{2}{3}}+400\times 23049601^{\frac{2}{3}}\right)}{1770578150416}\approx -0.333809541-2.757750342 \cdot 10^{-16}i$$

Solve for x

$$x=-\frac{250\sqrt{9602}\left(\sqrt{3}\sin(\frac{\arccos(\frac{\sqrt{9602}}{1000})}{3})+\cos(\frac{\arccos(\frac{\sqrt{9602}}{1000})}{3})\right)}{4801}\approx -8.666280144$$

$$x=\frac{500\sqrt{9602}\cos(\frac{\arccos(\frac{\sqrt{9602}}{1000})}{3})}{4801}\approx 9.000089686$$

$$x=\frac{250\sqrt{9602}\left(\sqrt{3}\sin(\frac{\arccos(\frac{\sqrt{9602}}{1000})}{3})-\cos(\frac{\arccos(\frac{\sqrt{9602}}{1000})}{3})\right)}{4801}\approx -0.333809541$$