G(x)=13x2+12x-7

Solution for G(x)=13x2+12x-7 equation:

(G)=13G^2+12G-7

We move all terms to the left:

(G)-(13G^2+12G-7)=0

We get rid of parentheses

-13G^2+G-12G+7=0

We add all the numbers together, and all the variables

-13G^2-11G+7=0

a = -13; b = -11; c = +7;
Δ = b2-4ac
Δ = -112-4·(-13)·7
Δ = 485
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{485}}{2*-13}=\frac{11-\sqrt{485}}{-26}
$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{485}}{2*-13}=\frac{11+\sqrt{485}}{-26}
$