(24-2x)(32-2x)=660

Solution for (24-2x)(32-2x)=660 equation:

(24-2x)(32-2x)=660

We move all terms to the left:

(24-2x)(32-2x)-(660)=0

We add all the numbers together, and all the variables

(-2x+24)(-2x+32)-660=0

We multiply parentheses ..

(+4x^2-64x-48x+768)-660=0

We get rid of parentheses

4x^2-64x-48x+768-660=0

We add all the numbers together, and all the variables

4x^2-112x+108=0

a = 4; b = -112; c = +108;
Δ = b2-4ac
Δ = -1122-4·4·108
Δ = 10816
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{10816}=104$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-112)-104}{2*4}=\frac{8}{8}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-112)+104}{2*4}=\frac{216}{8}
=27
$