2x/x+9=2x-9/x

Solution for 2x/x+9=2x-9/x equation:

2x/x+9=2x-9/x

We move all terms to the left:

2x/x+9-(2x-9/x)=0


Domain of the equation: 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

2x/x-(+2x-9/x)+9=0

We get rid of parentheses

2x/x-2x+9/x+9=0

We multiply all the terms by the denominator


2x-2x*x+9*x+9=0

We add all the numbers together, and all the variables

11x-2x*x+9=0

Wy multiply elements

-2x^2+11x+9=0

a = -2; b = 11; c = +9;
Δ = b2-4ac
Δ = 112-4·(-2)·9
Δ = 193
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-\sqrt{193}}{2*-2}=\frac{-11-\sqrt{193}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{193}}{2*-2}=\frac{-11+\sqrt{193}}{-4}
$