2x-1/2x=-28

Solution for 2x-1/2x=-28 equation:

2x-1/2x=-28

We move all terms to the left:

2x-1/2x-(-28)=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+28=0

We multiply all the terms by the denominator


2x*2x+28*2x-1=0

Wy multiply elements

4x^2+56x-1=0

a = 4; b = 56; c = -1;
Δ = b2-4ac
Δ = 562-4·4·(-1)
Δ = 3152
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:

$\sqrt{\Delta}=\sqrt{3152}=\sqrt{16*197}=\sqrt{16}*\sqrt{197}=4\sqrt{197}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(56)-4\sqrt{197}}{2*4}=\frac{-56-4\sqrt{197}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(56)+4\sqrt{197}}{2*4}=\frac{-56+4\sqrt{197}}{8}
$