Fisher's formula is essentially tautological.  It goes like this:
Q = the amount of economic goods that were bought with the currency, in a unit of value (say, a Big Mac, but it doesn't matter) in a given period
P = the price in units of our currency, of that unit of value (presumed stable enough during the period)

Clearly, Q . P = the amount of our currency that went over the counter to buy Q

M is the total amount of coins of our currency in existence (presumed fixed during the period)
We split that amount in different "kinds": m0 ; m1 ; m2 ; m3 .... mn so that their sum is M.

m0 are the coins that didn't move during this period (were held)

m1 are the coins that were spend once during this period

m2 are the coins that were spend twice: from A to B, and from B to C.

m3 are the coins that were spend three times

...

mn are the coins that were spend n times.

Clearly, the total amount of spendings, is:

m1 + 2 m2 + 3 m3 + ... + n mn

The total amount of spendings must be equal to the total amount of coins that went over the counter:

P . Q = m1 + 2 m2 + 3 m3 + .... + n mn

Now, define V = m1/M + 2 m2/M + 3 m3/M + ... n mn/M
which is the weighted average number of times a coin was spend during this period.

Then we have: P . Q = M . V


You shouldn't consider my critique of bitcoin as a critique of the idea to have a free currency.   My critique of bitcoin considers the bad design of it, not its pretended reason of existence.