27y-y^2=180

Solution for 27y-y^2=180 equation:

27y-y^2=180

We move all terms to the left:

27y-y^2-(180)=0

We add all the numbers together, and all the variables

-1y^2+27y-180=0

a = -1; b = 27; c = -180;
Δ = b2-4ac
Δ = 272-4·(-1)·(-180)
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-3}{2*-1}=\frac{-30}{-2}
=+15
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+3}{2*-1}=\frac{-24}{-2}
=+12
$