to balance a redox reaction like this, you first have to break it up into two half reactions with the reactants:
MnO4- --> Mn2+
Fe2+ --> Fe3+
then, you use electrons, h+, and water to balance them:
5e- + 8h+ + MnO4- --> Mn2+ + 4H2O
Fe2+ --> Fe3+ + e-
To cancel out the electrons, you have to multiply the iron half-reaction by 5. then you get this as the final reaction:
8H+ + 5Fe2+ + MnO4- --> 5Fe3+ + Mn2+ + 4H2O
5*3 + 2 = 17, the charge on the product side.
