2x+1/2x=4000

Solution for 2x+1/2x=4000 equation:

2x+1/2x=4000

We move all terms to the left:

2x+1/2x-(4000)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply all the terms by the denominator


2x*2x-4000*2x+1=0

Wy multiply elements

4x^2-8000x+1=0

a = 4; b = -8000; c = +1;
Δ = b2-4ac
Δ = -80002-4·4·1
Δ = 63999984
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:

$\sqrt{\Delta}=\sqrt{63999984}=\sqrt{16*3999999}=\sqrt{16}*\sqrt{3999999}=4\sqrt{3999999}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8000)-4\sqrt{3999999}}{2*4}=\frac{8000-4\sqrt{3999999}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8000)+4\sqrt{3999999}}{2*4}=\frac{8000+4\sqrt{3999999}}{8}
$