(12-y)y=15

Solution for (12-y)y=15 equation:

(12-y)y=15

We move all terms to the left:

(12-y)y-(15)=0

We add all the numbers together, and all the variables

(-1y+12)y-15=0

We multiply parentheses

-1y^2+12y-15=0

a = -1; b = 12; c = -15;
Δ = b2-4ac
Δ = 122-4·(-1)·(-15)
Δ = 84
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:

$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{21}}{2*-1}=\frac{-12-2\sqrt{21}}{-2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{21}}{2*-1}=\frac{-12+2\sqrt{21}}{-2}
$