Use the discriminant to tell whether the solutions of this equation are real or complex \[ 3 x^{2}-4 x+10=0 \]

Solve the equation \( 3x^2-4x+10=0 \). Solve the equation(The complex numbers system) by following steps: - step0: Solve using the quadratic formula in the complex numbers system: \(3x^{2}-4x+10=0\) - step1: Solve using the quadratic formula: \(x=\frac{4\pm \sqrt{\left(-4\right)^{2}-4\times 3\times 10}}{2\times 3}\) - step2: Simplify the expression: \(x=\frac{4\pm \sqrt{\left(-4\right)^{2}-4\times 3\times 10}}{6}\) - step3: Simplify the expression: \(x=\frac{4\pm \sqrt{-104}}{6}\) - step4: Simplify the expression: \(x=\frac{4\pm 2\sqrt{26}\times i}{6}\) - step5: Separate into possible cases: \(\begin{align}&x=\frac{4+2\sqrt{26}\times i}{6}\\&x=\frac{4-2\sqrt{26}\times i}{6}\end{align}\) - step6: Simplify the expression: \(\begin{align}&x=\frac{2}{3}+\frac{\sqrt{26}}{3}i\\&x=\frac{4-2\sqrt{26}\times i}{6}\end{align}\) - step7: Simplify the expression: \(\begin{align}&x=\frac{2}{3}+\frac{\sqrt{26}}{3}i\\&x=\frac{2}{3}-\frac{\sqrt{26}}{3}i\end{align}\) - step8: Rewrite: \(x_{1}=\frac{2}{3}-\frac{\sqrt{26}}{3}i,x_{2}=\frac{2}{3}+\frac{\sqrt{26}}{3}i\) - step9: Remove the complex number(s): \(\textrm{No real solution}\) The solutions of the equation \(3x^{2}-4x+10=0\) are complex. Therefore, the solutions are not real.