Solve \( 2 x^{2}+3 x+4=0 \) Give exact answer(s). If necessary, separate answers using a comma.

Solve the equation \( 2x^{2}+3x+4=0 \). Solve the equation(The complex numbers system) by following steps: - step0: Solve using the quadratic formula in the complex numbers system: \(2x^{2}+3x+4=0\) - step1: Solve using the quadratic formula: \(x=\frac{-3\pm \sqrt{3^{2}-4\times 2\times 4}}{2\times 2}\) - step2: Simplify the expression: \(x=\frac{-3\pm \sqrt{3^{2}-4\times 2\times 4}}{4}\) - step3: Simplify the expression: \(x=\frac{-3\pm \sqrt{-23}}{4}\) - step4: Simplify the expression: \(x=\frac{-3\pm \sqrt{23}\times i}{4}\) - step5: Separate into possible cases: \(\begin{align}&x=\frac{-3+\sqrt{23}\times i}{4}\\&x=\frac{-3-\sqrt{23}\times i}{4}\end{align}\) - step6: Simplify the expression: \(\begin{align}&x=-\frac{3}{4}+\frac{\sqrt{23}}{4}i\\&x=\frac{-3-\sqrt{23}\times i}{4}\end{align}\) - step7: Simplify the expression: \(\begin{align}&x=-\frac{3}{4}+\frac{\sqrt{23}}{4}i\\&x=-\frac{3}{4}-\frac{\sqrt{23}}{4}i\end{align}\) - step8: Rewrite: \(x_{1}=-\frac{3}{4}-\frac{\sqrt{23}}{4}i,x_{2}=-\frac{3}{4}+\frac{\sqrt{23}}{4}i\) - step9: Remove the complex number(s): \(\textrm{No real solution}\) The equation \(2x^{2}+3x+4=0\) does not have any real solutions. Therefore, there are no real values of \(x\) that satisfy this equation.