G(-2)=x^2+x-22

Solution for G(-2)=x^2+x-22 equation:

(-2)=G^2+G-22

We move all terms to the left:

(-2)-(G^2+G-22)=0

We add all the numbers together, and all the variables

-(G^2+G-22)-2=0

We get rid of parentheses

-G^2-G+22-2=0

We add all the numbers together, and all the variables

-1G^2-1G+20=0

a = -1; b = -1; c = +20;
Δ = b2-4ac
Δ = -12-4·(-1)·20
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$G_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$G_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-9}{2*-1}=\frac{-8}{-2}
=+4
$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+9}{2*-1}=\frac{10}{-2}
=-5
$