(15-2w)(12-2w)=108

Solution for (15-2w)(12-2w)=108 equation:

(15-2w)(12-2w)=108

We move all terms to the left:

(15-2w)(12-2w)-(108)=0

We add all the numbers together, and all the variables

(-2w+15)(-2w+12)-108=0

We multiply parentheses ..

(+4w^2-24w-30w+180)-108=0

We get rid of parentheses

4w^2-24w-30w+180-108=0

We add all the numbers together, and all the variables

4w^2-54w+72=0

a = 4; b = -54; c = +72;
Δ = b2-4ac
Δ = -542-4·4·72
Δ = 1764
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1764}=42$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-42}{2*4}=\frac{12}{8}
=1+1/2
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+42}{2*4}=\frac{96}{8}
=12
$