(8-2x)(16-2x)=48

Solution for (8-2x)(16-2x)=48 equation:

(8-2x)(16-2x)=48

We move all terms to the left:

(8-2x)(16-2x)-(48)=0

We add all the numbers together, and all the variables

(-2x+8)(-2x+16)-48=0

We multiply parentheses ..

(+4x^2-32x-16x+128)-48=0

We get rid of parentheses

4x^2-32x-16x+128-48=0

We add all the numbers together, and all the variables

4x^2-48x+80=0

a = 4; b = -48; c = +80;
Δ = b2-4ac
Δ = -482-4·4·80
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-32}{2*4}=\frac{16}{8}
=2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+32}{2*4}=\frac{80}{8}
=10
$