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

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

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

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

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

We calculate fractions


2x+(-9x)/3x+4x/3x-3=0

We multiply all the terms by the denominator


2x*3x+(-9x)+4x-3*3x=0

We add all the numbers together, and all the variables

4x+2x*3x+(-9x)-3*3x=0

Wy multiply elements

6x^2+4x+(-9x)-9x=0

We get rid of parentheses

6x^2+4x-9x-9x=0

We add all the numbers together, and all the variables

6x^2-14x=0

a = 6; b = -14; c = 0;
Δ = b2-4ac
Δ = -142-4·6·0
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-14}{2*6}=\frac{0}{12}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+14}{2*6}=\frac{28}{12}
=2+1/3
$