G(3)=x^2+5x-8

Solution for G(3)=x^2+5x-8 equation:

(3)=G^2+5G-8

We move all terms to the left:

(3)-(G^2+5G-8)=0

We get rid of parentheses

-G^2-5G+8+3=0

We add all the numbers together, and all the variables

-1G^2-5G+11=0

a = -1; b = -5; c = +11;
Δ = b2-4ac
Δ = -52-4·(-1)·11
Δ = 69
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{-(-5)-\sqrt{69}}{2*-1}=\frac{5-\sqrt{69}}{-2}
$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{69}}{2*-1}=\frac{5+\sqrt{69}}{-2}
$