(12+2x)(8+2x)=320

Solution for (12+2x)(8+2x)=320 equation:

(12+2x)(8+2x)=320

We move all terms to the left:

(12+2x)(8+2x)-(320)=0

We add all the numbers together, and all the variables

(2x+12)(2x+8)-320=0

We multiply parentheses ..

(+4x^2+16x+24x+96)-320=0

We get rid of parentheses

4x^2+16x+24x+96-320=0

We add all the numbers together, and all the variables

4x^2+40x-224=0

a = 4; b = 40; c = -224;
Δ = b2-4ac
Δ = 402-4·4·(-224)
Δ = 5184
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5184}=72$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-72}{2*4}=\frac{-112}{8}
=-14
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+72}{2*4}=\frac{32}{8}
=4
$