X+2/x-9=0

Solution for X+2/x-9=0 equation:

X+2/X-9=0


Domain of the equation: X!=0

X∈R


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 = 73
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{73}}{2*1}=\frac{9-\sqrt{73}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{73}}{2*1}=\frac{9+\sqrt{73}}{2}
$