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

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

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

We move all terms to the left:

x-5/2x+1-(x+2/x)=0


Domain of the equation: 2x!=0

x!=0/2

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-5/2x-(+x+2/x)+1=0

We get rid of parentheses

x-5/2x-x-2/x+1=0

We calculate fractions


x-x+(-5x)/2x^2+(-4x)/2x^2+1=0

We add all the numbers together, and all the variables

(-5x)/2x^2+(-4x)/2x^2+1=0

We multiply all the terms by the denominator


(-5x)+(-4x)+1*2x^2=0

Wy multiply elements

2x^2+(-5x)+(-4x)=0

We get rid of parentheses

2x^2-5x-4x=0

We add all the numbers together, and all the variables

2x^2-9x=0

a = 2; b = -9; c = 0;
Δ = b2-4ac
Δ = -92-4·2·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-9}{2*2}=\frac{0}{4}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+9}{2*2}=\frac{18}{4}
=4+1/2
$