90(y-30)y=180

Solution for 90(y-30)y=180 equation:

90(y-30)y=180

We move all terms to the left:

90(y-30)y-(180)=0

We multiply parentheses

90y^2-2700y-180=0

a = 90; b = -2700; c = -180;
Δ = b2-4ac
Δ = -27002-4·90·(-180)
Δ = 7354800
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{7354800}=\sqrt{32400*227}=\sqrt{32400}*\sqrt{227}=180\sqrt{227}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2700)-180\sqrt{227}}{2*90}=\frac{2700-180\sqrt{227}}{180}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2700)+180\sqrt{227}}{2*90}=\frac{2700+180\sqrt{227}}{180}
$