x-2/4x+1=x+5/x

Solution for x-2/4x+1=x+5/x equation:

x-2/4x+1=x+5/x

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

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

We get rid of parentheses

x-2/4x-x-5/x+1=0

We calculate fractions


x-x+(-2x)/4x^2+(-20x)/4x^2+1=0

We add all the numbers together, and all the variables

(-2x)/4x^2+(-20x)/4x^2+1=0

We multiply all the terms by the denominator


(-2x)+(-20x)+1*4x^2=0

Wy multiply elements

4x^2+(-2x)+(-20x)=0

We get rid of parentheses

4x^2-2x-20x=0

We add all the numbers together, and all the variables

4x^2-22x=0

a = 4; b = -22; c = 0;
Δ = b2-4ac
Δ = -222-4·4·0
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-22}{2*4}=\frac{0}{8}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+22}{2*4}=\frac{44}{8}
=5+1/2
$