Water with a tiny amount of washing up liquid works well (a teaspoonful to the tank of water.) We have a VAX and that works fine for us. Plain water works almost as well. If you do buy the detergent make sure you dilute it to least 5x the dose they tell you. They make their money from selling the detergent so they try to get you to use far more than you need.
Seriously, try it with just water and a tiny splash of washing up liquid, if it does not work you have lost nothing. If not get the cheapest machine carpet cleaning detergent and use 1/5th the recommended amount.