x-1+x-1+4x/(2x-1)+4x/(2x-1)=8

Solution for x-1+x-1+4x/(2x-1)+4x/(2x-1)=8 equation:

x-1+x-1+4x/(2x-1)+4x/(2x-1)=8

We move all terms to the left:

x-1+x-1+4x/(2x-1)+4x/(2x-1)-(8)=0


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

We move all terms containing x to the left, all other terms to the right

2x!=1

x!=1/2

x!=1/2

x∈R


We add all the numbers together, and all the variables

2x+4x/(2x-1)+4x/(2x-1)-10=0

We multiply all the terms by the denominator


2x*(2x-1)+4x+4x-10*(2x-1)=0

We add all the numbers together, and all the variables

8x+2x*(2x-1)-10*(2x-1)=0

We multiply parentheses

4x^2+8x-2x-20x+10=0

We add all the numbers together, and all the variables

4x^2-14x+10=0

a = 4; b = -14; c = +10;
Δ = b2-4ac
Δ = -142-4·4·10
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-6}{2*4}=\frac{8}{8}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+6}{2*4}=\frac{20}{8}
=2+1/2
$