2x+1/2x=3400

Solution for 2x+1/2x=3400 equation:

2x+1/2x=3400

We move all terms to the left:

2x+1/2x-(3400)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply all the terms by the denominator


2x*2x-3400*2x+1=0

Wy multiply elements

4x^2-6800x+1=0

a = 4; b = -6800; c = +1;
Δ = b2-4ac
Δ = -68002-4·4·1
Δ = 46239984
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:

$\sqrt{\Delta}=\sqrt{46239984}=\sqrt{1296*35679}=\sqrt{1296}*\sqrt{35679}=36\sqrt{35679}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6800)-36\sqrt{35679}}{2*4}=\frac{6800-36\sqrt{35679}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6800)+36\sqrt{35679}}{2*4}=\frac{6800+36\sqrt{35679}}{8}
$