Solve this

 Given:

$x^{2}-x+2=0$

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

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

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

$\Rightarrow x=\frac{1 \pm \sqrt{1-8}}{2}$

$\Rightarrow x=\frac{1 \pm \sqrt{-7}}{2}$

$\Rightarrow x=\frac{1 \pm \sqrt{7} i}{2}$

$\Rightarrow \quad x=\frac{1}{2} \pm \frac{\sqrt{7}}{2} i$

Ans: $x=\frac{1}{2}+\frac{\sqrt{7}}{2} i$ and $x=\frac{1}{2}-\frac{\sqrt{7}}{2} i$