to \( 3 x^{2}-2 x+4=0 \) ?

Solve the equation \( 3x^{2}-2x+4=0 \). Solve the equation(The complex numbers system) by following steps: - step0: Solve using the quadratic formula in the complex numbers system: \(3x^{2}-2x+4=0\) - step1: Solve using the quadratic formula: \(x=\frac{2\pm \sqrt{\left(-2\right)^{2}-4\times 3\times 4}}{2\times 3}\) - step2: Simplify the expression: \(x=\frac{2\pm \sqrt{\left(-2\right)^{2}-4\times 3\times 4}}{6}\) - step3: Simplify the expression: \(x=\frac{2\pm \sqrt{-44}}{6}\) - step4: Simplify the expression: \(x=\frac{2\pm 2\sqrt{11}\times i}{6}\) - step5: Separate into possible cases: \(\begin{align}&x=\frac{2+2\sqrt{11}\times i}{6}\\&x=\frac{2-2\sqrt{11}\times i}{6}\end{align}\) - step6: Simplify the expression: \(\begin{align}&x=\frac{1}{3}+\frac{\sqrt{11}}{3}i\\&x=\frac{2-2\sqrt{11}\times i}{6}\end{align}\) - step7: Simplify the expression: \(\begin{align}&x=\frac{1}{3}+\frac{\sqrt{11}}{3}i\\&x=\frac{1}{3}-\frac{\sqrt{11}}{3}i\end{align}\) - step8: Rewrite: \(x_{1}=\frac{1}{3}-\frac{\sqrt{11}}{3}i,x_{2}=\frac{1}{3}+\frac{\sqrt{11}}{3}i\) - step9: Remove the complex number(s): \(\textrm{No real solution}\) The equation \(3x^{2}-2x+4=0\) has no real solutions.