G(x)=X^2+12x+2

Solution for G(x)=X^2+12x+2 equation:

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-1G^2-11G-2=0

a = -1; b = -11; c = -2;
Δ = b2-4ac
Δ = -112-4·(-1)·(-2)
Δ = 113
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{-(-11)-\sqrt{113}}{2*-1}=\frac{11-\sqrt{113}}{-2}
$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{113}}{2*-1}=\frac{11+\sqrt{113}}{-2}
$