G(x)=4x^2-484.

Solution for G(x)=4x^2-484. equation:

(G)=4G^2-484.

We move all terms to the left:

(G)-(4G^2-484.)=0

We get rid of parentheses

-4G^2+G+484.=0

We add all the numbers together, and all the variables

-4G^2+G+484=0

a = -4; b = 1; c = +484;
Δ = b2-4ac
Δ = 12-4·(-4)·484
Δ = 7745
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{7745}}{2*-4}=\frac{-1-\sqrt{7745}}{-8}
$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{7745}}{2*-4}=\frac{-1+\sqrt{7745}}{-8}
$