Solve this

Given:

$x^{2}+3 x+5=0$

Solution of a general quadratic equation $a x^{2}+b x+c=0$ is given by:

$x=\frac{-b \pm \sqrt{\left(b^{2}-4 a c\right)}}{2 a}$

$\Rightarrow x=\frac{-3 \pm \sqrt{(3)^{2}-(4 \times 1 \times 5)}}{2 \times 1}$

$\Rightarrow x=\frac{-3 \pm \sqrt{9-20}}{2}$

$\Rightarrow \quad x=\frac{-3 \pm \sqrt{-11}}{2}$

$\Rightarrow x=\frac{-3 \pm \sqrt{11 i}}{2}$

$x=-\frac{3}{2} \pm \frac{\sqrt{11}}{2} i$

Ans: $x=-\frac{3}{2}+\frac{\sqrt{11}}{2} i$ and $x=-\frac{3}{2}-\frac{\sqrt{11}}{2} i$