-y^2+3y=9y-9

Solution for -y^2+3y=9y-9 equation:

-y^2+3y=9y-9

We move all terms to the left:

-y^2+3y-(9y-9)=0

We add all the numbers together, and all the variables

-1y^2+3y-(9y-9)=0

We get rid of parentheses

-1y^2+3y-9y+9=0

We add all the numbers together, and all the variables

-1y^2-6y+9=0

a = -1; b = -6; c = +9;
Δ = b2-4ac
Δ = -62-4·(-1)·9
Δ = 72
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:

$\sqrt{\Delta}=\sqrt{72}=\sqrt{36*2}=\sqrt{36}*\sqrt{2}=6\sqrt{2}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6\sqrt{2}}{2*-1}=\frac{6-6\sqrt{2}}{-2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6\sqrt{2}}{2*-1}=\frac{6+6\sqrt{2}}{-2}
$