x-6/3x+5=x+4/x

Solution for x-6/3x+5=x+4/x equation:

x-6/3x+5=x+4/x

We move all terms to the left:

x-6/3x+5-(x+4/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+4/x)+5=0

We get rid of parentheses

x-6/3x-x-4/x+5=0

We calculate fractions


x-x+(-6x)/3x^2+(-12x)/3x^2+5=0

We add all the numbers together, and all the variables

(-6x)/3x^2+(-12x)/3x^2+5=0

We multiply all the terms by the denominator


(-6x)+(-12x)+5*3x^2=0

Wy multiply elements

15x^2+(-6x)+(-12x)=0

We get rid of parentheses

15x^2-6x-12x=0

We add all the numbers together, and all the variables

15x^2-18x=0

a = 15; b = -18; c = 0;
Δ = b2-4ac
Δ = -182-4·15·0
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-18}{2*15}=\frac{0}{30}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+18}{2*15}=\frac{36}{30}
=1+1/5
$