192=(10+2x)(12+2x)

Solution for 192=(10+2x)(12+2x) equation:

192=(10+2x)(12+2x)

We move all terms to the left:

192-((10+2x)(12+2x))=0

We add all the numbers together, and all the variables

-((2x+10)(2x+12))+192=0

We multiply parentheses ..

-((+4x^2+24x+20x+120))+192=0


We calculate terms in parentheses: -((+4x^2+24x+20x+120)), so:

(+4x^2+24x+20x+120)

We get rid of parentheses

4x^2+24x+20x+120

We add all the numbers together, and all the variables

4x^2+44x+120

Back to the equation:

-(4x^2+44x+120)


We get rid of parentheses

-4x^2-44x-120+192=0

We add all the numbers together, and all the variables

-4x^2-44x+72=0

a = -4; b = -44; c = +72;
Δ = b2-4ac
Δ = -442-4·(-4)·72
Δ = 3088
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{3088}=\sqrt{16*193}=\sqrt{16}*\sqrt{193}=4\sqrt{193}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-44)-4\sqrt{193}}{2*-4}=\frac{44-4\sqrt{193}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-44)+4\sqrt{193}}{2*-4}=\frac{44+4\sqrt{193}}{-8}
$