G(x)=3x^2+2x-7

Solution for G(x)=3x^2+2x-7 equation:

(G)=3G^2+2G-7

We move all terms to the left:

(G)-(3G^2+2G-7)=0

We get rid of parentheses

-3G^2+G-2G+7=0

We add all the numbers together, and all the variables

-3G^2-1G+7=0

a = -3; b = -1; c = +7;
Δ = b2-4ac
Δ = -12-4·(-3)·7
Δ = 85
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{85}}{2*-3}=\frac{1-\sqrt{85}}{-6}
$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{85}}{2*-3}=\frac{1+\sqrt{85}}{-6}
$