For example, let's use secp256k1, the curve used by bitcoin, y^2 = x^3 + 7, and x=12. Over the real numbers, that calculation is trivial - I can simply use a calculator. But in a finite field, how does it work? If I say "X is 12", how do I calculate Y? The equation (when using real numbers) almost always results in fractions. And modulo P only works with integers.