G(x)=4x^2-12x

Solution for G(x)=4x^2-12x equation:

(G)=4G^2-12G

We move all terms to the left:

(G)-(4G^2-12G)=0

We get rid of parentheses

-4G^2+G+12G=0

We add all the numbers together, and all the variables

-4G^2+13G=0

a = -4; b = 13; c = 0;
Δ = b2-4ac
Δ = 132-4·(-4)·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$G_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$G_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-13}{2*-4}=\frac{-26}{-8}
=3+1/4
$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+13}{2*-4}=\frac{0}{-8}
=0
$