3y(y-2)=12y

Solution for 3y(y-2)=12y equation:

3y(y-2)=12y

We move all terms to the left:

3y(y-2)-(12y)=0

We add all the numbers together, and all the variables

-12y+3y(y-2)=0

We multiply parentheses

3y^2-12y-6y=0

We add all the numbers together, and all the variables

3y^2-18y=0

a = 3; b = -18; c = 0;
Δ = b2-4ac
Δ = -182-4·3·0
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-18}{2*3}=\frac{0}{6}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+18}{2*3}=\frac{36}{6}
=6
$