G(x)=x^2-7x-30

Solution for G(x)=x^2-7x-30 equation:

(G)=G^2-7G-30

We move all terms to the left:

(G)-(G^2-7G-30)=0

We get rid of parentheses

-G^2+G+7G+30=0

We add all the numbers together, and all the variables

-1G^2+8G+30=0

a = -1; b = 8; c = +30;
Δ = b2-4ac
Δ = 82-4·(-1)·30
Δ = 184
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:

$\sqrt{\Delta}=\sqrt{184}=\sqrt{4*46}=\sqrt{4}*\sqrt{46}=2\sqrt{46}$
$G_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{46}}{2*-1}=\frac{-8-2\sqrt{46}}{-2}
$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{46}}{2*-1}=\frac{-8+2\sqrt{46}}{-2}
$