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

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

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

We move all terms to the left:

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

We multiply parentheses

3x^2-36x-(2x-12)=0

We get rid of parentheses

3x^2-36x-2x+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}
$