180y-4y^2+72=180

Solution for 180y-4y^2+72=180 equation:

180y-4y^2+72=180

We move all terms to the left:

180y-4y^2+72-(180)=0

We add all the numbers together, and all the variables

-4y^2+180y-108=0

a = -4; b = 180; c = -108;
Δ = b2-4ac
Δ = 1802-4·(-4)·(-108)
Δ = 30672
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:

$\sqrt{\Delta}=\sqrt{30672}=\sqrt{144*213}=\sqrt{144}*\sqrt{213}=12\sqrt{213}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(180)-12\sqrt{213}}{2*-4}=\frac{-180-12\sqrt{213}}{-8}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(180)+12\sqrt{213}}{2*-4}=\frac{-180+12\sqrt{213}}{-8}
$