(108-2x)(144-2x)=7776

Solution for (108-2x)(144-2x)=7776 equation:

(108-2x)(144-2x)=7776

We move all terms to the left:

(108-2x)(144-2x)-(7776)=0

We add all the numbers together, and all the variables

(-2x+108)(-2x+144)-7776=0

We multiply parentheses ..

(+4x^2-288x-216x+15552)-7776=0

We get rid of parentheses

4x^2-288x-216x+15552-7776=0

We add all the numbers together, and all the variables

4x^2-504x+7776=0

a = 4; b = -504; c = +7776;
Δ = b2-4ac
Δ = -5042-4·4·7776
Δ = 129600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{129600}=360$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-504)-360}{2*4}=\frac{144}{8}
=18
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-504)+360}{2*4}=\frac{864}{8}
=108
$