G(x)=2x2+4x-12

Solution for G(x)=2x2+4x-12 equation:

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-2G^2-3G+12=0

a = -2; b = -3; c = +12;
Δ = b2-4ac
Δ = -32-4·(-2)·12
Δ = 105
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{-(-3)-\sqrt{105}}{2*-2}=\frac{3-\sqrt{105}}{-4}
$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{105}}{2*-2}=\frac{3+\sqrt{105}}{-4}
$