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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

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

a = -1; b = -1; c = +3;
Δ = b2-4ac
Δ = -12-4·(-1)·3
Δ = 13
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{13}}{2*-1}=\frac{1-\sqrt{13}}{-2}
$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{13}}{2*-1}=\frac{1+\sqrt{13}}{-2}
$