WHat kind of a wall, and how big? Not to meantion WHERE because labor rates vary greatly.

Bearing wall or not?
Wood studs? Drywall? Old lath and plaster? Paneling?
How many feet wide and high?
Wiring and plumbing in the wall?
First determine if it's a bearing wall, because if it is you may decide it's not worth paying for a beam and for propping up the joists on either side while installing it. It usually will be the wall down the middle of the house the long way, but there can be other places too. Measure thicknesses of walls around your house - the bearing wall(s) will be the thicker ones by and inch, generally.
Plumbing in the wall will usually cost you more to move than wiring will.
If you decide to proceed:
One way to save - remove wall covering carefully at eye level all along the wall to see what's what, and then get an exact quote in writing including debris removal and how much finish work is done (flooring, baseboards, ceiling mouldings, paint)..
Another way to save - buy some thin plastic tarp and move away from the wall and cover all your furniture in both rooms.
With a Sawzall, hammer, and prybar you could do the demolition yourself (on a non bearing wall).