ដោះស្រាយ 4x^3-6x+1=0

$$4 { x }^{ 3 } -6x+1 = 0$$

ដោះស្រាយសម្រាប់ x (complex solution)

$$x=-\frac{\left(-1+\sqrt{7}i\right)^{-\frac{1}{3}}\left(1+\sqrt{3}i\right)\left(-\sqrt{3}i\left(-1+\sqrt{7}i\right)^{\frac{2}{3}}-\left(-1+\sqrt{7}i\right)^{\frac{2}{3}}+4\right)}{8}\approx -1.300839566-1.110223025 \cdot 10^{-16}i$$

$$x=\frac{\left(-1+\sqrt{7}i\right)^{-\frac{1}{3}}\left(\left(-1+\sqrt{7}i\right)^{\frac{2}{3}}+2\right)}{2}\approx 1.130901123+1.110223025 \cdot 10^{-16}i$$

$$x=-\frac{\left(-1+\sqrt{7}i\right)^{-\frac{1}{3}}\left(-\sqrt{3}i+1\right)\left(\sqrt{3}i\left(-1+\sqrt{7}i\right)^{\frac{2}{3}}-\left(-1+\sqrt{7}i\right)^{\frac{2}{3}}+4\right)}{8}\approx 0.169938443+1.179611964 \cdot 10^{-16}i$$

ដោះស្រាយសម្រាប់ x

$$x=-\sqrt{2}\cos(\frac{\arccos(\frac{\sqrt{2}}{4})}{3})\approx -1.300839566$$

$$x=\frac{\sqrt{2}\cos(\frac{\arccos(\frac{\sqrt{2}}{4})}{3})+\sqrt{6}\sin(\frac{\arccos(\frac{\sqrt{2}}{4})}{3})}{2}\approx 1.130901123$$

$$x=\frac{\sqrt{2}\cos(\frac{\arccos(\frac{\sqrt{2}}{4})}{3})-\sqrt{6}\sin(\frac{\arccos(\frac{\sqrt{2}}{4})}{3})}{2}\approx 0.169938443$$