X/2x-6=2/x-4

Solution for X/2x-6=2/x-4 equation:

X/2X-6=2/X-4

We move all terms to the left:

X/2X-6-(2/X-4)=0


Domain of the equation: 2X!=0

X!=0/2

X!=0

X∈R



Domain of the equation: X-4)!=0

X∈R


We get rid of parentheses

X/2X-2/X+4-6=0

We calculate fractions


X^2/2X^2+(-4X)/2X^2+4-6=0

We add all the numbers together, and all the variables

X^2/2X^2+(-4X)/2X^2-2=0

We multiply all the terms by the denominator


X^2+(-4X)-2*2X^2=0

Wy multiply elements

X^2-4X^2+(-4X)=0

We get rid of parentheses

X^2-4X^2-4X=0

We add all the numbers together, and all the variables

-3X^2-4X=0

a = -3; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·(-3)·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4}{2*-3}=\frac{0}{-6}
=0
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*-3}=\frac{8}{-6}
=-1+1/3
$