2x-1=4/2x-1

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

2x-1=4/2x-1

We move all terms to the left:

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


Domain of the equation: 2x-1)!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


2x*2x+1*2x-1*2x-4=0

Wy multiply elements

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

We add all the numbers together, and all the variables

4x^2-4=0

a = 4; b = 0; c = -4;
Δ = b2-4ac
Δ = 02-4·4·(-4)
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8}{2*4}=\frac{-8}{8}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8}{2*4}=\frac{8}{8}
=1
$