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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 2x+4)!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

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

We add all the numbers together, and all the variables

-4x^2-16x+2=0

a = -4; b = -16; c = +2;
Δ = b2-4ac
Δ = -162-4·(-4)·2
Δ = 288
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{288}=\sqrt{144*2}=\sqrt{144}*\sqrt{2}=12\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-12\sqrt{2}}{2*-4}=\frac{16-12\sqrt{2}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+12\sqrt{2}}{2*-4}=\frac{16+12\sqrt{2}}{-8}
$