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 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 = 3120
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:

$\sqrt{\Delta}=\sqrt{3120}=\sqrt{16*195}=\sqrt{16}*\sqrt{195}=4\sqrt{195}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-56)-4\sqrt{195}}{2*4}=\frac{56-4\sqrt{195}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-56)+4\sqrt{195}}{2*4}=\frac{56+4\sqrt{195}}{8}
$