9-3y(y-2)=3-3y

Solution for 9-3y(y-2)=3-3y equation:

9-3y(y-2)=3-3y

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

-3y^2+6y-(-3y+3)+9=0

We get rid of parentheses

-3y^2+6y+3y-3+9=0

We add all the numbers together, and all the variables

-3y^2+9y+6=0

a = -3; b = 9; c = +6;
Δ = b2-4ac
Δ = 92-4·(-3)·6
Δ = 153
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:

$\sqrt{\Delta}=\sqrt{153}=\sqrt{9*17}=\sqrt{9}*\sqrt{17}=3\sqrt{17}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-3\sqrt{17}}{2*-3}=\frac{-9-3\sqrt{17}}{-6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+3\sqrt{17}}{2*-3}=\frac{-9+3\sqrt{17}}{-6}
$