Solve using the quadratic formula. \( 3 x^{2}+4 x+10=0 \)

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: \(x=\frac{-4\pm \sqrt{4^{2}-4\times 3\times 10}}{2\times 3}\) - step2: Simplify the expression: \(x=\frac{-4\pm \sqrt{4^{2}-4\times 3\times 10}}{6}\) - 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 quadratic equation \(3x^{2}+4x+10=0\) does not have any real solutions. This means that the equation has no real roots.