$2{x}^{2}+4x+3=0$
Identify the coefficients $a$, $b$ and $c$ of the quadratic equation$\begin{array} { l }a=2,& b=4,& c=3\end{array}$
Substitute $a=2$, $b=4$ and $c=3$ into the quadratic formula $x=\frac{ -b\pm\sqrt{ {b}^{2}-4ac } }{ 2a }$$x=\frac{ -4\pm\sqrt{ {4}^{2}-4 \times 2 \times 3 } }{ 2 \times 2 }$
Evaluate the power$x=\frac{ -4\pm\sqrt{ 16-4 \times 2 \times 3 } }{ 2 \times 2 }$
Calculate the product$x=\frac{ -4\pm\sqrt{ 16-24 } }{ 2 \times 2 }$
Multiply the numbers$x=\frac{ -4\pm\sqrt{ 16-24 } }{ 4 }$
Calculate the difference$x=\frac{ -4\pm\sqrt{ -8 } }{ 4 }$
The square root of a negative number does not exist in the set of real numbers$x\notin ℝ$