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

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

X-4/4X+1=X+5/X

We move all terms to the left:

X-4/4X+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-4/4X-(+X+5/X)+1=0

We get rid of parentheses

X-4/4X-X-5/X+1=0

We calculate fractions


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

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We get rid of parentheses

4X^2-4X-20X=0

We add all the numbers together, and all the variables

4X^2-24X=0

a = 4; b = -24; c = 0;
Δ = b2-4ac
Δ = -242-4·4·0
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-24}{2*4}=\frac{0}{8}
=0
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+24}{2*4}=\frac{48}{8}
=6
$