192=(12+2x)(8+2x)

Solution for 192=(12+2x)(8+2x) equation:

192=(12+2x)(8+2x)

We move all terms to the left:

192-((12+2x)(8+2x))=0

We add all the numbers together, and all the variables

-((2x+12)(2x+8))+192=0

We multiply parentheses ..

-((+4x^2+16x+24x+96))+192=0


We calculate terms in parentheses: -((+4x^2+16x+24x+96)), so:

(+4x^2+16x+24x+96)

We get rid of parentheses

4x^2+16x+24x+96

We add all the numbers together, and all the variables

4x^2+40x+96

Back to the equation:

-(4x^2+40x+96)


We get rid of parentheses

-4x^2-40x-96+192=0

We add all the numbers together, and all the variables

-4x^2-40x+96=0

a = -4; b = -40; c = +96;
Δ = b2-4ac
Δ = -402-4·(-4)·96
Δ = 3136
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3136}=56$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-56}{2*-4}=\frac{-16}{-8}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+56}{2*-4}=\frac{96}{-8}
=-12
$