(12+2x)(26+2x)=147

Solution for (12+2x)(26+2x)=147 equation:

(12+2x)(26+2x)=147

We move all terms to the left:

(12+2x)(26+2x)-(147)=0

We add all the numbers together, and all the variables

(2x+12)(2x+26)-147=0

We multiply parentheses ..

(+4x^2+52x+24x+312)-147=0

We get rid of parentheses

4x^2+52x+24x+312-147=0

We add all the numbers together, and all the variables

4x^2+76x+165=0

a = 4; b = 76; c = +165;
Δ = b2-4ac
Δ = 762-4·4·165
Δ = 3136
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3136}=56$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(76)-56}{2*4}=\frac{-132}{8}
=-16+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(76)+56}{2*4}=\frac{-20}{8}
=-2+1/2
$