396=(13+x)(17+x)

Solution for 396=(13+x)(17+x) equation:

396=(13+x)(17+x)

We move all terms to the left:

396-((13+x)(17+x))=0

We add all the numbers together, and all the variables

-((x+13)(x+17))+396=0

We multiply parentheses ..

-((+x^2+17x+13x+221))+396=0


We calculate terms in parentheses: -((+x^2+17x+13x+221)), so:

(+x^2+17x+13x+221)

We get rid of parentheses

x^2+17x+13x+221

We add all the numbers together, and all the variables

x^2+30x+221

Back to the equation:

-(x^2+30x+221)


We get rid of parentheses

-x^2-30x-221+396=0

We add all the numbers together, and all the variables

-1x^2-30x+175=0

a = -1; b = -30; c = +175;
Δ = b2-4ac
Δ = -302-4·(-1)·175
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-40}{2*-1}=\frac{-10}{-2}
=+5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+40}{2*-1}=\frac{70}{-2}
=-35
$