w(w-3)=180

Solution for w(w-3)=180 equation:

w(w-3)=180

We move all terms to the left:

w(w-3)-(180)=0

We multiply parentheses

w^2-3w-180=0

a = 1; b = -3; c = -180;
Δ = b2-4ac
Δ = -32-4·1·(-180)
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-27}{2*1}=\frac{-24}{2}
=-12
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+27}{2*1}=\frac{30}{2}
=15
$