G(x)=(x+9)(x-2)

Solution for G(x)=(x+9)(x-2) equation:

(G)=(G+9)(G-2)

We move all terms to the left:

(G)-((G+9)(G-2))=0

We multiply parentheses ..

-((+G^2-2G+9G-18))+G=0


We calculate terms in parentheses: -((+G^2-2G+9G-18)), so:

(+G^2-2G+9G-18)

We get rid of parentheses

G^2-2G+9G-18

We add all the numbers together, and all the variables

G^2+7G-18

Back to the equation:

-(G^2+7G-18)


We add all the numbers together, and all the variables

G-(G^2+7G-18)=0

We get rid of parentheses

-G^2+G-7G+18=0

We add all the numbers together, and all the variables

-1G^2-6G+18=0

a = -1; b = -6; c = +18;
Δ = b2-4ac
Δ = -62-4·(-1)·18
Δ = 108
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:

$\sqrt{\Delta}=\sqrt{108}=\sqrt{36*3}=\sqrt{36}*\sqrt{3}=6\sqrt{3}$
$G_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6\sqrt{3}}{2*-1}=\frac{6-6\sqrt{3}}{-2}
$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6\sqrt{3}}{2*-1}=\frac{6+6\sqrt{3}}{-2}
$