2x-1/2x-4=16

Solution for 2x-1/2x-4=16 equation:

2x-1/2x-4=16

We move all terms to the left:

2x-1/2x-4-(16)=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-1/2x-20=0

We multiply all the terms by the denominator


2x*2x-20*2x-1=0

Wy multiply elements

4x^2-40x-1=0

a = 4; b = -40; c = -1;
Δ = b2-4ac
Δ = -402-4·4·(-1)
Δ = 1616
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:

$\sqrt{\Delta}=\sqrt{1616}=\sqrt{16*101}=\sqrt{16}*\sqrt{101}=4\sqrt{101}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-4\sqrt{101}}{2*4}=\frac{40-4\sqrt{101}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+4\sqrt{101}}{2*4}=\frac{40+4\sqrt{101}}{8}
$