For electrons to balance properly, three moles of H must be oxidised for every mole of NO₃^- reduced:

3 (+1) + (-3) = 0

and the reaction can be written



In any reaction in aqueous solution, one is at liberty to assume as many H₂O,
H⁺, or OH^- as are required to balance the reaction, using H₂O and H⁺ under acidic conditions, or and OH^- if the solution is basic. The redox (oxidation - reduction) part of the balancing has been done, and what remains is only an accounting for O and H atoms. One possible answer is



This has accounted for the three hydrogen atoms and the negative charge. The equation is correct for basic solutions where OH^- ions are present.