(x-9)(x+3)=36

Solution for (x-9)(x+3)=36 equation:

(x-9)(x+3)=36

We move all terms to the left:

(x-9)(x+3)-(36)=0

We multiply parentheses ..

(+x^2+3x-9x-27)-36=0

We get rid of parentheses

x^2+3x-9x-27-36=0

We add all the numbers together, and all the variables

x^2-6x-63=0

a = 1; b = -6; c = -63;
Δ = b2-4ac
Δ = -62-4·1·(-63)
Δ = 288
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{288}=\sqrt{144*2}=\sqrt{144}*\sqrt{2}=12\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-12\sqrt{2}}{2*1}=\frac{6-12\sqrt{2}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+12\sqrt{2}}{2*1}=\frac{6+12\sqrt{2}}{2}
$