Force on table/chair rolling back

[Entr0py]

Homework Statement

Today I was sitting in a chair (with wheels on bottom) and decided to apply a force to a large desk. While I applied this force with my hand, my seat and I rolled backwards. My question is why is this so? I was thinking that if my hand is object "a" then it exerts a force on the desk (object "b"), F(ab) while the desk exerts a force F(ba) on my hand. Now if these action-reaction forces are equal and opposite then why do I accelerate backwards (or away from my desk)? What I think happens is that I DO accelerate the table but why can't I see its acceleration?

Homework Equations

Newton's third law and ΣF=ma where F and a are vectors

The Attempt at a Solution

 

[Titan97]

This is a common misconception. Even if actions reaction forces are equal and opposite, they are acting on two different bodies. The force you exert acts on the table. The table exerts an equal and opposite force on you. Hence for you, there is an unbalanced force acting on your body.