x-6/3x+8=x+5/x

Solution for x-6/3x+8=x+5/x equation:

x-6/3x+8=x+5/x

We move all terms to the left:

x-6/3x+8-(x+5/x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x-6/3x-(+x+5/x)+8=0

We get rid of parentheses

x-6/3x-x-5/x+8=0

We calculate fractions


x-x+(-6x)/3x^2+(-15x)/3x^2+8=0

We add all the numbers together, and all the variables

(-6x)/3x^2+(-15x)/3x^2+8=0

We multiply all the terms by the denominator


(-6x)+(-15x)+8*3x^2=0

Wy multiply elements

24x^2+(-6x)+(-15x)=0

We get rid of parentheses

24x^2-6x-15x=0

We add all the numbers together, and all the variables

24x^2-21x=0

a = 24; b = -21; c = 0;
Δ = b2-4ac
Δ = -212-4·24·0
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-21}{2*24}=\frac{0}{48}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+21}{2*24}=\frac{42}{48}
=7/8
$