Why do we need equal number of constraints and parameters to have a solution?

Question

While going through Shankar's Principles of Quantum Mechanics (2nd edition), in the Chapter 5 at page 179, while explaining the concept of quantization of energy for particle in a box he argued (though I may be wrong) that we need equal amount of parameters and constraints to have a solution. I want to understand why do we need so. Also what if there are more parameters than given constraints? I am also attaching the picture of the said page.