Question:
Solve the equation $-x^{2}+x-2=0$
Solution:
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
$\frac{-b \pm \sqrt{D}}{2 a}=\frac{-1 \pm \sqrt{-7}}{2 \times(-1)}=\frac{-1 \pm \sqrt{7} i}{-2}$ $[\sqrt{-1}=i]$