504=(2x+12)(2x+22)

Solution for 504=(2x+12)(2x+22) equation:

504=(2x+12)(2x+22)

We move all terms to the left:

504-((2x+12)(2x+22))=0

We multiply parentheses ..

-((+4x^2+44x+24x+264))+504=0


We calculate terms in parentheses: -((+4x^2+44x+24x+264)), so:

(+4x^2+44x+24x+264)

We get rid of parentheses

4x^2+44x+24x+264

We add all the numbers together, and all the variables

4x^2+68x+264

Back to the equation:

-(4x^2+68x+264)


We get rid of parentheses

-4x^2-68x-264+504=0

We add all the numbers together, and all the variables

-4x^2-68x+240=0

a = -4; b = -68; c = +240;
Δ = b2-4ac
Δ = -682-4·(-4)·240
Δ = 8464
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{8464}=92$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-68)-92}{2*-4}=\frac{-24}{-8}
=+3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-68)+92}{2*-4}=\frac{160}{-8}
=-20
$