2x-4=8+x/2x=

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

2x-4=8+x/2x=

We move all terms to the left:

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


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

2x-x/2x-8-4=0

We multiply all the terms by the denominator


2x*2x-x-8*2x-4*2x=0

We add all the numbers together, and all the variables

-1x+2x*2x-8*2x-4*2x=0

Wy multiply elements

4x^2-1x-16x-8x=0

We add all the numbers together, and all the variables

4x^2-25x=0

a = 4; b = -25; c = 0;
Δ = b2-4ac
Δ = -252-4·4·0
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-25}{2*4}=\frac{0}{8}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+25}{2*4}=\frac{50}{8}
=6+1/4
$