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

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

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

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


8x/2x^2+(-1x-6)/2x^2-1=0

We multiply all the terms by the denominator


8x+(-1x-6)-1*2x^2=0

Wy multiply elements

-2x^2+8x+(-1x-6)=0

We get rid of parentheses

-2x^2+8x-1x-6=0

We add all the numbers together, and all the variables

-2x^2+7x-6=0

a = -2; b = 7; c = -6;
Δ = b2-4ac
Δ = 72-4·(-2)·(-6)
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-1}{2*-2}=\frac{-8}{-4}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+1}{2*-2}=\frac{-6}{-4}
=1+1/2
$