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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

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


We calculate terms in parentheses: -((+4x^2+30x+24x+180)), so:

(+4x^2+30x+24x+180)

We get rid of parentheses

4x^2+30x+24x+180

We add all the numbers together, and all the variables

4x^2+54x+180

Back to the equation:

-(4x^2+54x+180)


We get rid of parentheses

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