(15+2x)(12+2x)=378

Solution for (15+2x)(12+2x)=378 equation:

(15+2x)(12+2x)=378

We move all terms to the left:

(15+2x)(12+2x)-(378)=0

We add all the numbers together, and all the variables

(2x+15)(2x+12)-378=0

We multiply parentheses ..

(+4x^2+24x+30x+180)-378=0

We get rid of parentheses

4x^2+24x+30x+180-378=0

We add all the numbers together, and all the variables

4x^2+54x-198=0

a = 4; b = 54; c = -198;
Δ = b2-4ac
Δ = 542-4·4·(-198)
Δ = 6084
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6084}=78$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-78}{2*4}=\frac{-132}{8}
=-16+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+78}{2*4}=\frac{24}{8}
=3
$