12x(x-12=3x)

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

12x(x-12=3x)

We move all terms to the left:

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

We add all the numbers together, and all the variables

12x(-2x-12)=0

We multiply parentheses

-24x^2-144x=0

a = -24; b = -144; c = 0;
Δ = b2-4ac
Δ = -1442-4·(-24)·0
Δ = 20736
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{20736}=144$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-144)-144}{2*-24}=\frac{0}{-48}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-144)+144}{2*-24}=\frac{288}{-48}
=-6
$