(12+2x)(15+2x)=304

Solution for (12+2x)(15+2x)=304 equation:

(12+2x)(15+2x)=304

We move all terms to the left:

(12+2x)(15+2x)-(304)=0

We add all the numbers together, and all the variables

(2x+12)(2x+15)-304=0

We multiply parentheses ..

(+4x^2+30x+24x+180)-304=0

We get rid of parentheses

4x^2+30x+24x+180-304=0

We add all the numbers together, and all the variables

4x^2+54x-124=0

a = 4; b = 54; c = -124;
Δ = b2-4ac
Δ = 542-4·4·(-124)
Δ = 4900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4900}=70$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-70}{2*4}=\frac{-124}{8}
=-15+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+70}{2*4}=\frac{16}{8}
=2
$