다음을 풀어보세요: y=4x^3+2x^2-12x+3=0

$$y=4 { x }^{ 3 } +2 { x }^{ 2 } -12x+3=0$$

x에 대한 해

$$x=\frac{\sqrt{37}\left(-\sqrt{3}\sin(\frac{\arccos(\frac{136\sqrt{37}}{1369})}{3})+\cos(\frac{\arccos(\frac{136\sqrt{37}}{1369})}{3})\right)-1}{6}$$

$$x=\frac{\sqrt{37}\left(\sqrt{3}\sin(\frac{\arccos(\frac{136\sqrt{37}}{1369})}{3})+\cos(\frac{\arccos(\frac{136\sqrt{37}}{1369})}{3})\right)-1}{6}$$

$$x=\frac{-2\sqrt{37}\cos(\frac{\arccos(\frac{136\sqrt{37}}{1369})}{3})-1}{6}\text{, }y=0$$

y에 대한 해

$$\left\{\begin{matrix}y=\frac{37\sqrt{37}\left(\sqrt{3}\sin(\frac{\arccos(\frac{136\sqrt{37}}{1369})}{3})+\cos(\frac{\arccos(\frac{136\sqrt{37}}{1369})}{3})\right)^{3}-111\sqrt{37}\cos(\frac{\arccos(\frac{136\sqrt{37}}{1369})}{3})-111\sqrt{111}\sin(\frac{\arccos(\frac{136\sqrt{37}}{1369})}{3})+272}{54}\text{, }&x=\frac{2\sqrt{37}\cos(\frac{-\arccos(\frac{136\sqrt{37}}{1369})+\pi }{3})-1}{6}\\y=\frac{-148\sqrt{37}\left(\cos(\frac{\arccos(\frac{136\sqrt{37}}{1369})}{3})\right)^{3}+111\sqrt{37}\cos(\frac{\arccos(\frac{136\sqrt{37}}{1369})}{3})+136}{27}\text{, }&x=\frac{-2\sqrt{37}\cos(\frac{\arccos(\frac{136\sqrt{37}}{1369})}{3})-1}{6}\\y=\frac{333\sqrt{37}\cos(\frac{\arccos(\frac{136\sqrt{37}}{1369})}{3})\left(\sin(\frac{\arccos(\frac{136\sqrt{37}}{1369})}{3})\right)^{2}+37\sqrt{37}\left(\cos(\frac{\arccos(\frac{136\sqrt{37}}{1369})}{3})\right)^{3}-111\sqrt{37}\cos(\frac{\arccos(\frac{136\sqrt{37}}{1369})}{3})+272}{54}\text{, }&x=\frac{2\sqrt{37}\cos(\frac{-\arccos(\frac{136\sqrt{37}}{1369})+5\pi }{3})-1}{6}\end{matrix}\right.$$