12-4/3x=2x

Solution for 12-4/3x=2x equation:

12-4/3x=2x

We move all terms to the left:

12-4/3x-(2x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

-2x-4/3x+12=0

We multiply all the terms by the denominator


-2x*3x+12*3x-4=0

Wy multiply elements

-6x^2+36x-4=0

a = -6; b = 36; c = -4;
Δ = b2-4ac
Δ = 362-4·(-6)·(-4)
Δ = 1200
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:

$\sqrt{\Delta}=\sqrt{1200}=\sqrt{400*3}=\sqrt{400}*\sqrt{3}=20\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-20\sqrt{3}}{2*-6}=\frac{-36-20\sqrt{3}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+20\sqrt{3}}{2*-6}=\frac{-36+20\sqrt{3}}{-12}
$