Solve this

Given:

$\sqrt{5} \mathrm{x}^{2}+\mathrm{x}+\sqrt{5}=0$

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

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

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

$\Rightarrow x=\frac{-1 \pm \sqrt{1-20}}{2 \sqrt{5}}$

$x=\frac{-1 \pm \sqrt{-19}}{2 \sqrt{5}}$

$\Rightarrow \quad x=\frac{-1 \pm \sqrt{19} i}{2 \sqrt{5}}$

$\Rightarrow x=-\frac{1}{2 \sqrt{5}} \pm \frac{\sqrt{19}}{2 \sqrt{5}} i$

Ans: $x=-\frac{\sqrt{5}}{10}+\frac{\sqrt{\frac{19}{5}}}{2} i$ and $x=-\frac{\sqrt{5}}{10}-\frac{\sqrt{\frac{19}{5}}}{2} i$