G(x)=2x^2+2x-12=-8

Solution for G(x)=2x^2+2x-12=-8 equation:

(G)=2G^2+2G-12=-8

We move all terms to the left:

(G)-(2G^2+2G-12)=0

We get rid of parentheses

-2G^2+G-2G+12=0

We add all the numbers together, and all the variables

-2G^2-1G+12=0

a = -2; b = -1; c = +12;
Δ = b2-4ac
Δ = -12-4·(-2)·12
Δ = 97
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$G_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$G_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{97}}{2*-2}=\frac{1-\sqrt{97}}{-4}
$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{97}}{2*-2}=\frac{1+\sqrt{97}}{-4}
$