(12+2x)(10+2x)=255

Solution for (12+2x)(10+2x)=255 equation:

(12+2x)(10+2x)=255

We move all terms to the left:

(12+2x)(10+2x)-(255)=0

We add all the numbers together, and all the variables

(2x+12)(2x+10)-255=0

We multiply parentheses ..

(+4x^2+20x+24x+120)-255=0

We get rid of parentheses

4x^2+20x+24x+120-255=0

We add all the numbers together, and all the variables

4x^2+44x-135=0

a = 4; b = 44; c = -135;
Δ = b2-4ac
Δ = 442-4·4·(-135)
Δ = 4096
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4096}=64$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(44)-64}{2*4}=\frac{-108}{8}
=-13+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(44)+64}{2*4}=\frac{20}{8}
=2+1/2
$