(13+w)(17+w)=396

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

(13+w)(17+w)=396

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

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

We get rid of parentheses

w^2+17w+13w+221-396=0

We add all the numbers together, and all the variables

w^2+30w-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:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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