Momentum before the action = Momentum after
So:
Where m1 and v1 are for the gun and m2 and v2 are for the bullet
(initial side) m1v1 + m2v2 = m1v1 + m2v2 (final side)
Initially there is no momentum so we are left with
0 = m1v1 + m2v2 (final)
Subtract over m1v1
-m1v1 = m2v2
We are looking for v1 which is the final velocity of the gun
so:
v1 = m2v2 / -m1
v1 = (15 x 10^-3 kg)(840) / -(3.5)
v1 = -3.6 m/s
The negative indicates that it is travelling in the negative direction towards the shooter
