w(2w-6)=180

Solution for w(2w-6)=180 equation:

w(2w-6)=180

We move all terms to the left:

w(2w-6)-(180)=0

We multiply parentheses

2w^2-6w-180=0

a = 2; b = -6; c = -180;
Δ = b2-4ac
Δ = -62-4·2·(-180)
Δ = 1476
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:

$\sqrt{\Delta}=\sqrt{1476}=\sqrt{36*41}=\sqrt{36}*\sqrt{41}=6\sqrt{41}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6\sqrt{41}}{2*2}=\frac{6-6\sqrt{41}}{4}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6\sqrt{41}}{2*2}=\frac{6+6\sqrt{41}}{4}
$