If a force of 50 N stretches a spring 0.10 m, what is the spring constant? 
 
I know that if you double the weight you double the force but i do not
know what the equation for the spring constant is.

Search google for Hookes law.
://www.google.com/search?num=20&complete=1&hl=en&lr=&newwindow=1&safe=off&q=hookes+law&btnG=Search

To first order in x, that is, linear in x... springs are described by Hooke's law:

F = -k*DeltaX

This equation has a lot of assumptions importantly a spring confined
to 1D-motion.  But basically it just says that the force required to
compress or stretch the spring in one direction by DeltaX is directly
and linearly proportional to the displacement DeltaX.  So the constant
"k" is a measure of how strong the spring is, a bigger k means a lot
more force is going to be required to stretch/compress the spring..
think shocks on a car.. and a smaller k means less force... think
rubberband, I guess.

Hope that helps...