15y=12y(y-3)

Solution for 15y=12y(y-3) equation:

15y=12y(y-3)

We move all terms to the left:

15y-(12y(y-3))=0


We calculate terms in parentheses: -(12y(y-3)), so:

12y(y-3)

We multiply parentheses

12y^2-36y

Back to the equation:

-(12y^2-36y)


We get rid of parentheses

-12y^2+15y+36y=0

We add all the numbers together, and all the variables

-12y^2+51y=0

a = -12; b = 51; c = 0;
Δ = b2-4ac
Δ = 512-4·(-12)·0
Δ = 2601
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2601}=51$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(51)-51}{2*-12}=\frac{-102}{-24}
=4+1/4
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(51)+51}{2*-12}=\frac{0}{-24}
=0
$