3y(y-3)=(y-3)

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

3y(y-3)=(y-3)

We move all terms to the left:

3y(y-3)-((y-3))=0

We multiply parentheses

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


We calculate terms in parentheses: -((y-3)), so:

(y-3)

We get rid of parentheses

y-3

Back to the equation:

-(y-3)


We get rid of parentheses

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

We add all the numbers together, and all the variables

3y^2-10y+3=0

a = 3; b = -10; c = +3;
Δ = b2-4ac
Δ = -102-4·3·3
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-8}{2*3}=\frac{2}{6}
=1/3
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+8}{2*3}=\frac{18}{6}
=3
$