G(-3)=3x^2+4x-7

Solution for G(-3)=3x^2+4x-7 equation:

(-3)=3G^2+4G-7

We move all terms to the left:

(-3)-(3G^2+4G-7)=0

We add all the numbers together, and all the variables

-(3G^2+4G-7)-3=0

We get rid of parentheses

-3G^2-4G+7-3=0

We add all the numbers together, and all the variables

-3G^2-4G+4=0

a = -3; b = -4; c = +4;
Δ = b2-4ac
Δ = -42-4·(-3)·4
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$G_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$G_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-8}{2*-3}=\frac{-4}{-6}
=2/3
$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+8}{2*-3}=\frac{12}{-6}
=-2
$