2/4x-1=6/x-2

Solution for 2/4x-1=6/x-2 equation:

2/4x-1=6/x-2

We move all terms to the left:

2/4x-1-(6/x-2)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: x-2)!=0

x∈R


We get rid of parentheses

2/4x-6/x+2-1=0

We calculate fractions


2x/4x^2+(-24x)/4x^2+2-1=0

We add all the numbers together, and all the variables

2x/4x^2+(-24x)/4x^2+1=0

We multiply all the terms by the denominator


2x+(-24x)+1*4x^2=0

Wy multiply elements

4x^2+2x+(-24x)=0

We get rid of parentheses

4x^2+2x-24x=0

We add all the numbers together, and all the variables

4x^2-22x=0

a = 4; b = -22; c = 0;
Δ = b2-4ac
Δ = -222-4·4·0
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-22}{2*4}=\frac{0}{8}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+22}{2*4}=\frac{44}{8}
=5+1/2
$