G(x)=x^2+5x-11

Solution for G(x)=x^2+5x-11 equation:

(G)=G^2+5G-11

We move all terms to the left:

(G)-(G^2+5G-11)=0

We get rid of parentheses

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

We add all the numbers together, and all the variables

-1G^2-4G+11=0

a = -1; b = -4; c = +11;
Δ = b2-4ac
Δ = -42-4·(-1)·11
Δ = 60
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:

$\sqrt{\Delta}=\sqrt{60}=\sqrt{4*15}=\sqrt{4}*\sqrt{15}=2\sqrt{15}$
$G_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{15}}{2*-1}=\frac{4-2\sqrt{15}}{-2}
$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{15}}{2*-1}=\frac{4+2\sqrt{15}}{-2}
$