x+6/x-9=9/x

Solution for x+6/x-9=9/x equation:

x+6/x-9=9/x

We move all terms to the left:

x+6/x-9-(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

x+6/x-(+9/x)-9=0

We get rid of parentheses

x+6/x-9/x-9=0

We multiply all the terms by the denominator


x*x-9*x+6-9=0

We add all the numbers together, and all the variables

-9x+x*x-3=0

Wy multiply elements

x^2-9x-3=0

a = 1; b = -9; c = -3;
Δ = b2-4ac
Δ = -92-4·1·(-3)
Δ = 93
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{-(-9)-\sqrt{93}}{2*1}=\frac{9-\sqrt{93}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{93}}{2*1}=\frac{9+\sqrt{93}}{2}
$