G(x)=x^2-10x-4

Solution for G(x)=x^2-10x-4 equation:

(G)=G^2-10G-4

We move all terms to the left:

(G)-(G^2-10G-4)=0

We get rid of parentheses

-G^2+G+10G+4=0

We add all the numbers together, and all the variables

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

a = -1; b = 11; c = +4;
Δ = b2-4ac
Δ = 112-4·(-1)·4
Δ = 137
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{-(11)-\sqrt{137}}{2*-1}=\frac{-11-\sqrt{137}}{-2}
$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{137}}{2*-1}=\frac{-11+\sqrt{137}}{-2}
$