(12+2x)(26+2x)=1472

Solution for (12+2x)(26+2x)=1472 equation:

(12+2x)(26+2x)=1472

We move all terms to the left:

(12+2x)(26+2x)-(1472)=0

We add all the numbers together, and all the variables

(2x+12)(2x+26)-1472=0

We multiply parentheses ..

(+4x^2+52x+24x+312)-1472=0

We get rid of parentheses

4x^2+52x+24x+312-1472=0

We add all the numbers together, and all the variables

4x^2+76x-1160=0

a = 4; b = 76; c = -1160;
Δ = b2-4ac
Δ = 762-4·4·(-1160)
Δ = 24336
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{24336}=156$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(76)-156}{2*4}=\frac{-232}{8}
=-29
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(76)+156}{2*4}=\frac{80}{8}
=10
$