12y-y^2=24

Solution for 12y-y^2=24 equation:

12y-y^2=24

We move all terms to the left:

12y-y^2-(24)=0

We add all the numbers together, and all the variables

-1y^2+12y-24=0

a = -1; b = 12; c = -24;
Δ = b2-4ac
Δ = 122-4·(-1)·(-24)
Δ = 48
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:

$\sqrt{\Delta}=\sqrt{48}=\sqrt{16*3}=\sqrt{16}*\sqrt{3}=4\sqrt{3}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{3}}{2*-1}=\frac{-12-4\sqrt{3}}{-2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{3}}{2*-1}=\frac{-12+4\sqrt{3}}{-2}
$