550=(12+x)(15+x)

Solution for 550=(12+x)(15+x) equation:

550=(12+x)(15+x)

We move all terms to the left:

550-((12+x)(15+x))=0

We add all the numbers together, and all the variables

-((x+12)(x+15))+550=0

We multiply parentheses ..

-((+x^2+15x+12x+180))+550=0


We calculate terms in parentheses: -((+x^2+15x+12x+180)), so:

(+x^2+15x+12x+180)

We get rid of parentheses

x^2+15x+12x+180

We add all the numbers together, and all the variables

x^2+27x+180

Back to the equation:

-(x^2+27x+180)


We get rid of parentheses

-x^2-27x-180+550=0

We add all the numbers together, and all the variables

-1x^2-27x+370=0

a = -1; b = -27; c = +370;
Δ = b2-4ac
Δ = -272-4·(-1)·370
Δ = 2209
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2209}=47$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-47}{2*-1}=\frac{-20}{-2}
=+10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+47}{2*-1}=\frac{74}{-2}
=-37
$