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

Solution for (x-1)+(4x/2x-1)=4 equation:

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

We move all terms to the left:

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


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

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

2x^2+4x-2x-2x-8x=0

We add all the numbers together, and all the variables

2x^2-8x=0

a = 2; b = -8; c = 0;
Δ = b2-4ac
Δ = -82-4·2·0
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{-(-8)-8}{2*2}=\frac{0}{4}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8}{2*2}=\frac{16}{4}
=4
$