Question:
$2 x^{2}-\sqrt{3} x+1=0$
Solution:
Given:
$2 x^{2}-\sqrt{3} x+1=0$
Solution of a general quadratic equation $a x^{2}+b x+c=0$ is given by:
$x=\frac{-b \pm \sqrt{\left(b^{2}-4 a c\right)}}{2 a}$
$\Rightarrow x=\frac{-(-\sqrt{3}) \pm \sqrt{(-\sqrt{3})^{2}-(4 \times 2 \times 1)}}{2 \times 2}$
$\Rightarrow x=\frac{\sqrt{3} \pm \sqrt{3-8}}{4}$
$\Rightarrow x=\frac{\sqrt{3} \pm \sqrt{-5}}{4}$
$\Rightarrow \quad x=\frac{\sqrt{3} \pm \sqrt{5} i}{4}$
$\Rightarrow \quad x=\frac{\sqrt{3}}{4} \pm \frac{\sqrt{5}}{4} i$
Ans: $x=\frac{\sqrt{3}}{4}+\frac{\sqrt{5}}{4} i$ and $x=\frac{\sqrt{3}}{4}-\frac{\sqrt{5}}{4} i$