(20-2x)(12-2x)=84

Solution for (20-2x)(12-2x)=84 equation:

(20-2x)(12-2x)=84

We move all terms to the left:

(20-2x)(12-2x)-(84)=0

We add all the numbers together, and all the variables

(-2x+20)(-2x+12)-84=0

We multiply parentheses ..

(+4x^2-24x-40x+240)-84=0

We get rid of parentheses

4x^2-24x-40x+240-84=0

We add all the numbers together, and all the variables

4x^2-64x+156=0

a = 4; b = -64; c = +156;
Δ = b2-4ac
Δ = -642-4·4·156
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-64)-40}{2*4}=\frac{24}{8}
=3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-64)+40}{2*4}=\frac{104}{8}
=13
$