Solve the equation –x2 + x – 2 = 0

The given quadratic equation is $-x^{2}+x-2=0$

On comparing the given equation with $a x^{2}+b x+c=0$, we obtain

$a=-1, b=1$, and $c=-2$

Therefore, the discriminant of the given equation is

$D=b^{2}-4 a c=1^{2}-4 \times(-1) \times(-2)=1-8=-7$

Therefore, the required solutions are

$\frac{-b \pm \sqrt{D}}{2 a}=\frac{-1 \pm \sqrt{-7}}{2 \times(-1)}=\frac{-1 \pm \sqrt{7} i}{-2}$  $[\sqrt{-1}=i]$