12y-6-y^2=0

Solution for 12y-6-y^2=0 equation:

12y-6-y^2=0

We add all the numbers together, and all the variables

-1y^2+12y-6=0

a = -1; b = 12; c = -6;
Δ = b2-4ac
Δ = 122-4·(-1)·(-6)
Δ = 120
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:

$\sqrt{\Delta}=\sqrt{120}=\sqrt{4*30}=\sqrt{4}*\sqrt{30}=2\sqrt{30}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{30}}{2*-1}=\frac{-12-2\sqrt{30}}{-2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{30}}{2*-1}=\frac{-12+2\sqrt{30}}{-2}
$