G(x)=x^2-8

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

(G)=G^2-8

We move all terms to the left:

(G)-(G^2-8)=0

We get rid of parentheses

-G^2+G+8=0

We add all the numbers together, and all the variables

-1G^2+G+8=0

a = -1; b = 1; c = +8;
Δ = b2-4ac
Δ = 12-4·(-1)·8
Δ = 33
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{33}}{2*-1}=\frac{-1-\sqrt{33}}{-2}
$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{33}}{2*-1}=\frac{-1+\sqrt{33}}{-2}
$