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

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

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

We move all terms to the left:

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

x^2+12x-126=0

a = 1; b = 12; c = -126;
Δ = b2-4ac
Δ = 122-4·1·(-126)
Δ = 648
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:

$\sqrt{\Delta}=\sqrt{648}=\sqrt{324*2}=\sqrt{324}*\sqrt{2}=18\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-18\sqrt{2}}{2*1}=\frac{-12-18\sqrt{2}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+18\sqrt{2}}{2*1}=\frac{-12+18\sqrt{2}}{2}
$