Info[x_]  :=  x Log[x]/Log[2]

Info[x_]  :=  x Log[x]/Log[2]

H[x_]  :=  Info[x]  +  Info[1 - x]

f[d_, b_, n_, r_, e_]  :=  
      (1  -  2 Exp[- n (d^2) ]) 
        (r  -  
            Log[2,  1  +  
                Sqrt[2 n] 
                  2^(r  -  n ( H[e  -  d]  -  H[e]  +  b ))
                      ])

D[f[d, b, n, r, e] , d]

Solve[ %  ==  0, d]