How to calculate the amount of weight my plane can takeoff with?
Yes, you can do your equations at OEM (Operating Empty Mass) and get your ground distance. Then you can calculate the same for different mass values (your OEM+your payload), and generate a distance vs mass. Since you know how much distance you have (including any safety factors), you can see what mass you can take off with. Or work backwards from the same equation, set the maximum distance you allow, and work back to your mass value.

Keep in mind this will not tell you whether the airplane is structurally strong enough to carry that weight, only if it can take-off with it. Structural calculations are a bit more complex than this. Also, you might want to do similar calcs for landing distane as well!