Leadplant is on the right track.
The real question is what size is your breaker to the rooms in question.
Also, see if you can find the amperage draw on the AC and let us know.
Extension cords are the cheapest easiest way to do it, but they are a PITA and easy to trip over.
Upgrading the breaker w/o changing out the wiring is ASKING for trouble, so don't do that unless you replace all the wiring as well. A 15A circuit uses 14G wire and a 20 uses 12G wire. See if you can see some of the actual wiring for the circuit, and it will tell you on the wire if its 12 or 14. It will say something like "Romex 14-3 AWG" Which stands for 14 gauge, 3 wires. If you happen to get lucky, and you have a 15A breaker and 12G wiring, then I would def recommend you change out the breaker, but NOT in any other circumstanes.
Also, are you running 120V or 220/240V?
A better option than the ext cords is to run a subpanel to your grow area, and then run dedicated outlets to diff areas of the room.
Give us a total power consumption estimate including fans and pumps. If you don't know the wattage they use, tell us how many of each and what size you plan on using.
Even with no elec exp you can easily run a sub panel IF, and its a HUGE IF, IF you have a kill switch that shuts off the entire panel. They are usually located at the top of the box, of in a small box either above the panel, or somewhere between the meter and panel. If you don't have a kill switch than just use extension cords. The benefit of a sub panel is its easy to do yourself and you can run everything up to code except for having it done w/no permit, but its not too hard and with a little help from around here we'll have you in good shape :)
Be safe
I
also, Pm me a link back here when you respond, as I don't bookmark threads.