x-2/x-9=5/x

Solution for x-2/x-9=5/x equation:

x-2/x-9=5/x

We move all terms to the left:

x-2/x-9-(5/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-2/x-(+5/x)-9=0

We get rid of parentheses

x-2/x-5/x-9=0

We multiply all the terms by the denominator


x*x-9*x-2-5=0

We add all the numbers together, and all the variables

-9x+x*x-7=0

Wy multiply elements

x^2-9x-7=0

a = 1; b = -9; c = -7;
Δ = b2-4ac
Δ = -92-4·1·(-7)
Δ = 109
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{109}}{2*1}=\frac{9-\sqrt{109}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{109}}{2*1}=\frac{9+\sqrt{109}}{2}
$