96-6y=y*y

Solution for 96-6y=y*y equation:

96-6y=y*y

We move all terms to the left:

96-6y-(y*y)=0

We add all the numbers together, and all the variables

-6y-(+y*y)+96=0

We get rid of parentheses

-6y-y*y+96=0

Wy multiply elements

-1y^2-6y+96=0

a = -1; b = -6; c = +96;
Δ = b2-4ac
Δ = -62-4·(-1)·96
Δ = 420
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:

$\sqrt{\Delta}=\sqrt{420}=\sqrt{4*105}=\sqrt{4}*\sqrt{105}=2\sqrt{105}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{105}}{2*-1}=\frac{6-2\sqrt{105}}{-2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{105}}{2*-1}=\frac{6+2\sqrt{105}}{-2}
$