Find the roots of each of the following equations, if they exist, by applying the quadratic formula:

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

Comparing it with $a x^{2}+b x+c=0$, we get

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

$\therefore$ Discriminant, $D=b^{2}-4 a c=1^{2}-4 \times 1 \times 2=1-8=-7<0$

Hence, the given equation has no real roots (or real roots does not exist).