3y(y-2)=3y-6

Solution for 3y(y-2)=3y-6 equation:

3y(y-2)=3y-6

We move all terms to the left:

3y(y-2)-(3y-6)=0

We multiply parentheses

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

We get rid of parentheses

3y^2-6y-3y+6=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 = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-3}{2*3}=\frac{6}{6}
=1
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+3}{2*3}=\frac{12}{6}
=2
$