(18-2x)(12-2x)=108

Solution for (18-2x)(12-2x)=108 equation:

(18-2x)(12-2x)=108

We move all terms to the left:

(18-2x)(12-2x)-(108)=0

We add all the numbers together, and all the variables

(-2x+18)(-2x+12)-108=0

We multiply parentheses ..

(+4x^2-24x-36x+216)-108=0

We get rid of parentheses

4x^2-24x-36x+216-108=0

We add all the numbers together, and all the variables

4x^2-60x+108=0

a = 4; b = -60; c = +108;
Δ = b2-4ac
Δ = -602-4·4·108
Δ = 1872
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:

$\sqrt{\Delta}=\sqrt{1872}=\sqrt{144*13}=\sqrt{144}*\sqrt{13}=12\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-12\sqrt{13}}{2*4}=\frac{60-12\sqrt{13}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+12\sqrt{13}}{2*4}=\frac{60+12\sqrt{13}}{8}
$