12x-4/3x-1=x

Solution for 12x-4/3x-1=x equation:

12x-4/3x-1=x

We move all terms to the left:

12x-4/3x-1-(x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

11x-4/3x-1=0

We multiply all the terms by the denominator


11x*3x-1*3x-4=0

Wy multiply elements

33x^2-3x-4=0

a = 33; b = -3; c = -4;
Δ = b2-4ac
Δ = -32-4·33·(-4)
Δ = 537
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-\sqrt{537}}{2*33}=\frac{3-\sqrt{537}}{66}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{537}}{2*33}=\frac{3+\sqrt{537}}{66}
$