Simple statics...any physics book or statics book will show this to you.
Don't forget to include the weight of the beam as it might be significant for larger equipment.
How critical is this support system? It is important that such supports and connections be designed properly, as equipment downtime and safety are paramount to such designs.
I would suggest that you get a structural engineer involved. Even though your simplistic sketch shows a simple, fundamental analysis need, there are parameters that you have not shared with us that might not be appropriately considered if you only do the simple static analysis.