2x/x-2=x+8/3

Solution for 2x/x-2=x+8/3 equation:

2x/x-2=x+8/3

We move all terms to the left:

2x/x-2-(x+8/3)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

2x/x-(+x+8/3)-2=0

We get rid of parentheses

2x/x-x-2-8/3=0

We calculate fractions


-x+6x/3x+(-8x)/3x-2=0

We add all the numbers together, and all the variables

-1x+6x/3x+(-8x)/3x-2=0

We multiply all the terms by the denominator


-1x*3x+6x+(-8x)-2*3x=0

We add all the numbers together, and all the variables

6x-1x*3x+(-8x)-2*3x=0

Wy multiply elements

-3x^2+6x+(-8x)-6x=0

We get rid of parentheses

-3x^2+6x-8x-6x=0

We add all the numbers together, and all the variables

-3x^2-8x=0

a = -3; b = -8; c = 0;
Δ = b2-4ac
Δ = -82-4·(-3)·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8}{2*-3}=\frac{0}{-6}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8}{2*-3}=\frac{16}{-6}
=-2+2/3
$