(w+115)(4w+40)=180

Solution for (w+115)(4w+40)=180 equation:

(w+115)(4w+40)=180

We move all terms to the left:

(w+115)(4w+40)-(180)=0

We multiply parentheses ..

(+4w^2+40w+460w+4600)-180=0

We get rid of parentheses

4w^2+40w+460w+4600-180=0

We add all the numbers together, and all the variables

4w^2+500w+4420=0

a = 4; b = 500; c = +4420;
Δ = b2-4ac
Δ = 5002-4·4·4420
Δ = 179280
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{179280}=\sqrt{144*1245}=\sqrt{144}*\sqrt{1245}=12\sqrt{1245}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(500)-12\sqrt{1245}}{2*4}=\frac{-500-12\sqrt{1245}}{8}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(500)+12\sqrt{1245}}{2*4}=\frac{-500+12\sqrt{1245}}{8}
$