G(x)=3x^2-48

Solution for G(x)=3x^2-48 equation:

(G)=3G^2-48

We move all terms to the left:

(G)-(3G^2-48)=0

We get rid of parentheses

-3G^2+G+48=0

a = -3; b = 1; c = +48;
Δ = b2-4ac
Δ = 12-4·(-3)·48
Δ = 577
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{577}}{2*-3}=\frac{-1-\sqrt{577}}{-6}
$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{577}}{2*-3}=\frac{-1+\sqrt{577}}{-6}
$