How would I go about doing that (checking the charging system)?

 

The procedure is just a few posts back in this same thread, but we need to modify it a bit if your meter is still reading high:

Measure the battery voltage (fully charged) with the quad off. Start up the quad and measure the voltage at a fast engine clip with the headlights off. It should increase 0.8 to 1.8 volts above what you measured before the quad was started.