x+6/3=2x-8/x

Solution for x+6/3=2x-8/x equation:

x+6/3=2x-8/x

We move all terms to the left:

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


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

x-2x+8/x+2=0

We multiply all the terms by the denominator


x*x-2x*x+2*x+8=0

We add all the numbers together, and all the variables

2x+x*x-2x*x+8=0

Wy multiply elements

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

We add all the numbers together, and all the variables

-1x^2+2x+8=0

a = -1; b = 2; c = +8;
Δ = b2-4ac
Δ = 22-4·(-1)·8
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-6}{2*-1}=\frac{-8}{-2}
=+4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+6}{2*-1}=\frac{4}{-2}
=-2
$