w^2+13w+90=180

Solution for w^2+13w+90=180 equation:

w^2+13w+90=180

We move all terms to the left:

w^2+13w+90-(180)=0

We add all the numbers together, and all the variables

w^2+13w-90=0

a = 1; b = 13; c = -90;
Δ = b2-4ac
Δ = 132-4·1·(-90)
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-23}{2*1}=\frac{-36}{2}
=-18
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+23}{2*1}=\frac{10}{2}
=5
$