(x-6)(x+18)=72

Solution for (x-6)(x+18)=72 equation:

(x-6)(x+18)=72

We move all terms to the left:

(x-6)(x+18)-(72)=0

We multiply parentheses ..

(+x^2+18x-6x-108)-72=0

We get rid of parentheses

x^2+18x-6x-108-72=0

We add all the numbers together, and all the variables

x^2+12x-180=0

a = 1; b = 12; c = -180;
Δ = b2-4ac
Δ = 122-4·1·(-180)
Δ = 864
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:

$\sqrt{\Delta}=\sqrt{864}=\sqrt{144*6}=\sqrt{144}*\sqrt{6}=12\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-12\sqrt{6}}{2*1}=\frac{-12-12\sqrt{6}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+12\sqrt{6}}{2*1}=\frac{-12+12\sqrt{6}}{2}
$