1/2x-2=2-2/4x

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

1/2x-2=2-2/4x

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


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

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

8x-4*8x^2=0

Wy multiply elements

-32x^2+8x=0

a = -32; b = 8; c = 0;
Δ = b2-4ac
Δ = 82-4·(-32)·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*-32}=\frac{-16}{-64}
=1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8}{2*-32}=\frac{0}{-64}
=0
$