12y-y^2=27

Solution for 12y-y^2=27 equation:

12y-y^2=27

We move all terms to the left:

12y-y^2-(27)=0

We add all the numbers together, and all the variables

-1y^2+12y-27=0

a = -1; b = 12; c = -27;
Δ = b2-4ac
Δ = 122-4·(-1)·(-27)
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-6}{2*-1}=\frac{-18}{-2}
=+9
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+6}{2*-1}=\frac{-6}{-2}
=+3
$