A nucleus containing more than 83 protons will always be unstable, no matter how many neutrons there are, as there is just too much proton-proton repulsion.
For a nucleus with 83 or fewer protons, having too few neutrons than protons will be unstable. Also having too many neutrons than protons will also be unstable. But having the proper ratio of neutrons, approximately equal to or slightly greater than the number of protons, will make the nucleus stable.
Related to the weirdness of the strong force is that a proton (which is intrinsically stable) can be transformed into a neutron, and vice versa (through processes we'll discuss later). Even more weird is that a neutron is intrinsically unstable--an isolated neutron outside of a nucleus has a half-life of 10.2 minutes, and will eventually decay back into a proton. Think of a stable nucleus as having protons continuously transforming into neutrons, and neutrons continuously transforming into protons, and as they are transforming back and forth into each other, the strong force "sticks" them together, balancing the repulsive force between protons. An unstable nucleus, then, also has protons transforming into neutrons and vice versa, but the wrong ratio of protons to neutrons does not optimize the amount of proton-neutron transformations--and thus strong force "stickiness"--that would balance the repulsive force between protons, such that the nucleus will eventually need to somehow undergo a process to reach a more stable configuration, whether by falling apart (fission), or ejecting small parts of itself, as in the modes of radioactive decay discussed below.
(For the purposes of completing our discussion of beta decay, a third type is electron capture, where the nucleus will actually swallow an electron, in order to achieve a more stable configuration (and also emit a neutrino afterwards). Does this increase or decrease the number of nucleons in the nucleus? Does this increase or decrease the number of protons in the nucleus? Does this increase or decrease the number of neutrons in the nucleus? Is electron capture more similar to beta-minus decay or beta-plus decay?)