G(x)=x2+15x-54

Solution for G(x)=x2+15x-54 equation:

(G)=G2+15G-54

We move all terms to the left:

(G)-(G2+15G-54)=0

We add all the numbers together, and all the variables

-(+G^2+15G-54)+G=0

We get rid of parentheses

-G^2-15G+G+54=0

We add all the numbers together, and all the variables

-1G^2-14G+54=0

a = -1; b = -14; c = +54;
Δ = b2-4ac
Δ = -142-4·(-1)·54
Δ = 412
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:

$\sqrt{\Delta}=\sqrt{412}=\sqrt{4*103}=\sqrt{4}*\sqrt{103}=2\sqrt{103}$
$G_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{103}}{2*-1}=\frac{14-2\sqrt{103}}{-2}
$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{103}}{2*-1}=\frac{14+2\sqrt{103}}{-2}
$