4y(y+20)=180

Solution for 4y(y+20)=180 equation:

4y(y+20)=180

We move all terms to the left:

4y(y+20)-(180)=0

We multiply parentheses

4y^2+80y-180=0

a = 4; b = 80; c = -180;
Δ = b2-4ac
Δ = 802-4·4·(-180)
Δ = 9280
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:

$\sqrt{\Delta}=\sqrt{9280}=\sqrt{64*145}=\sqrt{64}*\sqrt{145}=8\sqrt{145}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(80)-8\sqrt{145}}{2*4}=\frac{-80-8\sqrt{145}}{8}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(80)+8\sqrt{145}}{2*4}=\frac{-80+8\sqrt{145}}{8}
$