X(3x-1)-12=4x

Solution for X(3x-1)-12=4x equation:

X(3X-1)-12=4X

We move all terms to the left:

X(3X-1)-12-(4X)=0

We add all the numbers together, and all the variables

-4X+X(3X-1)-12=0

We multiply parentheses

3X^2-4X-1X-12=0

We add all the numbers together, and all the variables

3X^2-5X-12=0

a = 3; b = -5; c = -12;
Δ = b2-4ac
Δ = -52-4·3·(-12)
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-13}{2*3}=\frac{-8}{6}
=-1+1/3
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+13}{2*3}=\frac{18}{6}
=3
$