This says
2^x -(2^1)/(2^x) - 1 = 0
So ....multiply through by 2^x =
2^(2x) -2 - 2^x = 0 rearrange
2^(2x) - 2^x - 2 = 0
This is a little hard to solve, but we can see that x = 1 is a solution ... [2^(2*1) - 2*(1) - 2] = [4 - 2 - 2 = 0]
Here's the graph from Desmos.....it indicates that this is the only "real" solution.....
https://www.desmos.com/calculator/v0raxp8fvh