Solve `sqrt(5)x^2+x+sqrt(5)=0` .

Answer

`x=frac{-1-sqrt{19} i}{2 sqrt{5}}`

Explanation

Given that quadratric equation is `\sqrt{5}x^{2}+x+\sqrt{5}=0`


[If given qudratics equation a `a^{2}+b x+c=0, then x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}` ]



Then we compare given quadratic equation with standrad form, we get `a = \sqrt{5}, b=1, c=\sqrt{5}`, then



\begin{aligned}
&x=\frac{-1 \pm \sqrt{1-(4 \times \sqrt{5} \times \sqrt{5})}}{2 \sqrt{5}} \\
...