I'm handling power plant maintenance and want to know about the technics of fan balancing.(with formulas)

You need a balance meter.

You need polar paper, ruler, vibration analyzer with phase measurement. Plot vibration mag. And phase on paper. Next you would add a trial weight that causes an imbalance force approx 10% of weight of rotor. Plot he new vib mag and phase. Now calculate the change you need to make new vib magnitude equal to original mag. And 180 opposite it.