(12+2x)(12+2x)=836

Solution for (12+2x)(12+2x)=836 equation:

(12+2x)(12+2x)=836

We move all terms to the left:

(12+2x)(12+2x)-(836)=0

We add all the numbers together, and all the variables

(2x+12)(2x+12)-836=0

We multiply parentheses ..

(+4x^2+24x+24x+144)-836=0

We get rid of parentheses

4x^2+24x+24x+144-836=0

We add all the numbers together, and all the variables

4x^2+48x-692=0

a = 4; b = 48; c = -692;
Δ = b2-4ac
Δ = 482-4·4·(-692)
Δ = 13376
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:

$\sqrt{\Delta}=\sqrt{13376}=\sqrt{64*209}=\sqrt{64}*\sqrt{209}=8\sqrt{209}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-8\sqrt{209}}{2*4}=\frac{-48-8\sqrt{209}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+8\sqrt{209}}{2*4}=\frac{-48+8\sqrt{209}}{8}
$