X/x-6=x-2/x

Solution for X/x-6=x-2/x equation:

X/X-6=X-2/X

We move all terms to the left:

X/X-6-(X-2/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/X-(+X-2/X)-6=0

We get rid of parentheses

X/X-X+2/X-6=0

Fractions to decimals

2/X-X-6+1=0

We multiply all the terms by the denominator


-X*X-6*X+1*X+2=0

We add all the numbers together, and all the variables

-5X-X*X+2=0

Wy multiply elements

-1X^2-5X+2=0

a = -1; b = -5; c = +2;
Δ = b2-4ac
Δ = -52-4·(-1)·2
Δ = 33
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{-(-5)-\sqrt{33}}{2*-1}=\frac{5-\sqrt{33}}{-2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{33}}{2*-1}=\frac{5+\sqrt{33}}{-2}
$