Ican apply a force on a cart to cause it to accelerate across the floor. but newton's third law says that for every force there is an equal and opposite force. so why isn't the cart in equilibrium?

So if you push a cart on the floor it will eventually slow down because of the friction. So if you add X amount of force there will be X amount of opposite force. So it would never be equal because something will always slow to cart down.