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!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

2x+4x/2x+4x/2x-12=0

We multiply all the terms by the denominator


2x*2x+4x+4x-12*2x=0

We add all the numbers together, and all the variables

8x+2x*2x-12*2x=0

Wy multiply elements

4x^2+8x-24x=0

We add all the numbers together, and all the variables

4x^2-16x=0

a = 4; b = -16; c = 0;
Δ = b2-4ac
Δ = -162-4·4·0
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-16}{2*4}=\frac{0}{8}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+16}{2*4}=\frac{32}{8}
=4
$