G(x+2)=5x^2+3x-4

Solution for G(x+2)=5x^2+3x-4 equation:

(G+2)=5G^2+3G-4

We move all terms to the left:

(G+2)-(5G^2+3G-4)=0

We get rid of parentheses

-5G^2+G-3G+2+4=0

We add all the numbers together, and all the variables

-5G^2-2G+6=0

a = -5; b = -2; c = +6;
Δ = b2-4ac
Δ = -22-4·(-5)·6
Δ = 124
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$G_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{124}=\sqrt{4*31}=\sqrt{4}*\sqrt{31}=2\sqrt{31}$
$G_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{31}}{2*-5}=\frac{2-2\sqrt{31}}{-10}
$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{31}}{2*-5}=\frac{2+2\sqrt{31}}{-10}
$