Question:
$x^{2}-x+2=0$
Solution:
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 $x=\frac{1}{2}-\frac{\sqrt{7}}{2} i$