(10+2x)(12+2x)=104

Solution for (10+2x)(12+2x)=104 equation:

(10+2x)(12+2x)=104

We move all terms to the left:

(10+2x)(12+2x)-(104)=0

We add all the numbers together, and all the variables

(2x+10)(2x+12)-104=0

We multiply parentheses ..

(+4x^2+24x+20x+120)-104=0

We get rid of parentheses

4x^2+24x+20x+120-104=0

We add all the numbers together, and all the variables

4x^2+44x+16=0

a = 4; b = 44; c = +16;
Δ = b2-4ac
Δ = 442-4·4·16
Δ = 1680
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:

$\sqrt{\Delta}=\sqrt{1680}=\sqrt{16*105}=\sqrt{16}*\sqrt{105}=4\sqrt{105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(44)-4\sqrt{105}}{2*4}=\frac{-44-4\sqrt{105}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(44)+4\sqrt{105}}{2*4}=\frac{-44+4\sqrt{105}}{8}
$