G(x)=5x^2-12

Solution for G(x)=5x^2-12 equation:

(G)=5G^2-12

We move all terms to the left:

(G)-(5G^2-12)=0

We get rid of parentheses

-5G^2+G+12=0

a = -5; b = 1; c = +12;
Δ = b2-4ac
Δ = 12-4·(-5)·12
Δ = 241
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{241}}{2*-5}=\frac{-1-\sqrt{241}}{-10}
$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{241}}{2*-5}=\frac{-1+\sqrt{241}}{-10}
$