x=2/x-9

Solution for x=2/x-9 equation:

x=2/x-9

We move all terms to the left:

x-(2/x-9)=0


Domain of the equation: x-9)!=0

x∈R


We get rid of parentheses

x-2/x+9=0

We multiply all the terms by the denominator


x*x+9*x-2=0

We add all the numbers together, and all the variables

9x+x*x-2=0

Wy multiply elements

x^2+9x-2=0

a = 1; b = 9; c = -2;
Δ = b2-4ac
Δ = 92-4·1·(-2)
Δ = 89
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{89}}{2*1}=\frac{-9-\sqrt{89}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{89}}{2*1}=\frac{-9+\sqrt{89}}{2}
$