Solve 4x^3-16x^2+7x+1=0

$$4 x ^ { 3 } - 16 x ^ { 2 } + 7 x + 1 = 0$$

Solve for x (complex solution)

$$x=\frac{\sqrt{3}i\sqrt[3]{233+3\sqrt{2802}i}}{12}-\frac{43\sqrt{3}i\left(233+3\sqrt{2802}i\right)^{-\frac{1}{3}}}{12}-\frac{\sqrt[3]{233+3\sqrt{2802}i}}{12}-\frac{43\left(233+3\sqrt{2802}i\right)^{-\frac{1}{3}}}{12}+\frac{4}{3}\approx -0.112900108-1.942890293 \cdot 10^{-16}i$$

$$x=\frac{\sqrt[3]{233+3\sqrt{2802}i}}{6}+\frac{43\left(233+3\sqrt{2802}i\right)^{-\frac{1}{3}}}{6}+\frac{4}{3}\approx 3.475830186-5.551115123 \cdot 10^{-17}i$$

$$x=-\frac{\sqrt{3}i\sqrt[3]{233+3\sqrt{2802}i}}{12}+\frac{43\sqrt{3}i\left(233+3\sqrt{2802}i\right)^{-\frac{1}{3}}}{12}-\frac{\sqrt[3]{233+3\sqrt{2802}i}}{12}-\frac{43\left(233+3\sqrt{2802}i\right)^{-\frac{1}{3}}}{12}+\frac{4}{3}\approx 0.637069922+2.498001805 \cdot 10^{-16}i$$

Solve for x

$$x=\frac{-\sqrt{43}\cos(\frac{\arccos(\frac{233\sqrt{43}}{1849})}{3})-\sqrt{129}\sin(\frac{\arccos(\frac{233\sqrt{43}}{1849})}{3})+8}{6}\approx -0.112900108$$

$$x=\frac{\sqrt{43}\cos(\frac{\arccos(\frac{233\sqrt{43}}{1849})}{3})+4}{3}\approx 3.475830186$$

$$x=\frac{\sqrt{129}\sin(\frac{\arccos(\frac{233\sqrt{43}}{1849})}{3})-\sqrt{43}\cos(\frac{\arccos(\frac{233\sqrt{43}}{1849})}{3})+8}{6}\approx 0.637069922$$