2x-12=3x(x-12)

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

2x-12=3x(x-12)

We move all terms to the left:

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


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

3x(x-12)

We multiply parentheses

3x^2-36x

Back to the equation:

-(3x^2-36x)


We get rid of parentheses

-3x^2+2x+36x-12=0

We add all the numbers together, and all the variables

-3x^2+38x-12=0

a = -3; b = 38; c = -12;
Δ = b2-4ac
Δ = 382-4·(-3)·(-12)
Δ = 1300
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1300}=\sqrt{100*13}=\sqrt{100}*\sqrt{13}=10\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(38)-10\sqrt{13}}{2*-3}=\frac{-38-10\sqrt{13}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(38)+10\sqrt{13}}{2*-3}=\frac{-38+10\sqrt{13}}{-6}
$