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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We calculate fractions


x-x+(-4x)/2x^2+(-10x)/2x^2+1=0

We add all the numbers together, and all the variables

(-4x)/2x^2+(-10x)/2x^2+1=0

We multiply all the terms by the denominator


(-4x)+(-10x)+1*2x^2=0

Wy multiply elements

2x^2+(-4x)+(-10x)=0

We get rid of parentheses

2x^2-4x-10x=0

We add all the numbers together, and all the variables

2x^2-14x=0

a = 2; b = -14; c = 0;
Δ = b2-4ac
Δ = -142-4·2·0
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-14}{2*2}=\frac{0}{4}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+14}{2*2}=\frac{28}{4}
=7
$