Yea, that is something that worried me a lot too but later on i understood.
See, the resultant force, if its is zero, then by newtons law (F = Ma)
F = 0 --> a = 0
acceleration is nothing but change in the velocity over time.
so, when a = 0, i.e' the change in velocity is zero. Not the velocity itself.
so, the velocity of the object before the forces getting balanced, if it is zero, then the object stays at rest
If the object was moving with some velocity prior to the forces becoming zero, it will continue with that velocity.
the most important thing you have to remember here is that acceleration is just the change of velocity, not the velocity itself.
Hope this helps. Have fun :)