Stability analysis using characteristic equation

Okay I am not an expert at matlab, infact I am quite the opposite but I have the following characteristic equation:

s^2 + y*s + n^2 + 1 - exp(-s*t) = 0

What I need from the stability analysis is two graphs with:

0.1 < t < 100 and 0.01 < n < 100 (first graph y=0 and second graph y=0.5)

but I am completely lost what to do. And for the graph the stable region should be given a dark colour and unstable in just white. Its asking a lot and maybe isn't possible from what I have given but I am at a complete loss because I don't know how to determine if its stable or not, is it to do with the roots?

[Jonathan Epperl]

You'll have to at least tell us, what y, s, n and t signify here. In particular y seems to be out of place in a "characteristic equation," which I would expect to be in terms of s and some parameters...

[jamie]

t is a time delay and y is a damping value, n is stiffness. The exp(-s*t) term is from a delayed term. Well for the two graphs y is going to be a constant, (0 for one and 0.5 for another)