X+9/2x+1=x-5/x

Solution for X+9/2x+1=x-5/x equation:

X+9/2X+1=X-5/X

We move all terms to the left:

X+9/2X+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+9/2X-(+X-5/X)+1=0

We get rid of parentheses

X+9/2X-X+5/X+1=0

We calculate fractions


X-X+9X/2X^2+10X/2X^2+1=0

We add all the numbers together, and all the variables

9X/2X^2+10X/2X^2+1=0

We multiply all the terms by the denominator


9X+10X+1*2X^2=0

We add all the numbers together, and all the variables

19X+1*2X^2=0

Wy multiply elements

2X^2+19X=0

a = 2; b = 19; c = 0;
Δ = b2-4ac
Δ = 192-4·2·0
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-19}{2*2}=\frac{-38}{4}
=-9+1/2
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+19}{2*2}=\frac{0}{4}
=0
$