15x=12x(x-3)

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

15x=12x(x-3)

We move all terms to the left:

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


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

12x(x-3)

We multiply parentheses

12x^2-36x

Back to the equation:

-(12x^2-36x)


We get rid of parentheses

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

We add all the numbers together, and all the variables

-12x^2+51x=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:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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