(8-x)(12-x)=32

Solution for (8-x)(12-x)=32 equation:

(8-x)(12-x)=32

We move all terms to the left:

(8-x)(12-x)-(32)=0

We add all the numbers together, and all the variables

(-1x+8)(-1x+12)-32=0

We multiply parentheses ..

(+x^2-12x-8x+96)-32=0

We get rid of parentheses

x^2-12x-8x+96-32=0

We add all the numbers together, and all the variables

x^2-20x+64=0

a = 1; b = -20; c = +64;
Δ = b2-4ac
Δ = -202-4·1·64
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-12}{2*1}=\frac{8}{2}
=4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+12}{2*1}=\frac{32}{2}
=16
$