3x/3+4/3-4x/x-4=x

Solution for 3x/3+4/3-4x/x-4=x equation:

3x/3+4/3-4x/x-4=x

We move all terms to the left:

3x/3+4/3-4x/x-4-(x)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

-1x+3x/3-4x/x-4+4/3=0

We calculate fractions


-1x+7x/3x+(-12x)/3x-4=0

We multiply all the terms by the denominator


-1x*3x+7x+(-12x)-4*3x=0

We add all the numbers together, and all the variables

7x-1x*3x+(-12x)-4*3x=0

Wy multiply elements

-3x^2+7x+(-12x)-12x=0

We get rid of parentheses

-3x^2+7x-12x-12x=0

We add all the numbers together, and all the variables

-3x^2-17x=0

a = -3; b = -17; c = 0;
Δ = b2-4ac
Δ = -172-4·(-3)·0
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-17}{2*-3}=\frac{0}{-6}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+17}{2*-3}=\frac{34}{-6}
=-5+2/3
$