(12+2x)(15+2x)=754

Solution for (12+2x)(15+2x)=754 equation:

(12+2x)(15+2x)=754

We move all terms to the left:

(12+2x)(15+2x)-(754)=0

We add all the numbers together, and all the variables

(2x+12)(2x+15)-754=0

We multiply parentheses ..

(+4x^2+30x+24x+180)-754=0

We get rid of parentheses

4x^2+30x+24x+180-754=0

We add all the numbers together, and all the variables

4x^2+54x-574=0

a = 4; b = 54; c = -574;
Δ = b2-4ac
Δ = 542-4·4·(-574)
Δ = 12100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{12100}=110$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-110}{2*4}=\frac{-164}{8}
=-20+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+110}{2*4}=\frac{56}{8}
=7
$