X-5/3x+1=x+2/x

Solution for X-5/3x+1=x+2/x equation:

X-5/3X+1=X+2/X

We move all terms to the left:

X-5/3X+1-(X+2/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-5/3X-(+X+2/X)+1=0

We get rid of parentheses

X-5/3X-X-2/X+1=0

We calculate fractions


X-X+(-5X)/3X^2+(-6X)/3X^2+1=0

We add all the numbers together, and all the variables

(-5X)/3X^2+(-6X)/3X^2+1=0

We multiply all the terms by the denominator


(-5X)+(-6X)+1*3X^2=0

Wy multiply elements

3X^2+(-5X)+(-6X)=0

We get rid of parentheses

3X^2-5X-6X=0

We add all the numbers together, and all the variables

3X^2-11X=0

a = 3; b = -11; c = 0;
Δ = b2-4ac
Δ = -112-4·3·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-11}{2*3}=\frac{0}{6}
=0
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+11}{2*3}=\frac{22}{6}
=3+2/3
$