intersection points of line on a circle

[TOdorus]

Hi all,

I have a bit of an algebraic problem, and my lack of attention during math is starting to show. I was experimenting with hit detection based on lines for a simple shooting game, and the enemies bieng circulair.

I already have a function to check the distance from the line to the circles centre, so I already know that there is a intersection (or hit). I also would like to know where it intersects, for graphics and some extra physics.

So here's what I got:

Known:
r
m
b

so these can be considered constant

Equitions so far

y = mx+b
r^2 = y^2 + x^2

this gives:
r^2 = (mx+b)^2 + x^2

And then my troubles begin, because writing that out would give:
r^2 + b^2 = x^2 + mx^2 + 2mbx

Googling around tells me that this is the way to go, and you should get a quadratic function, but I don't know how to solve this kind of equation. Can anybody help out? I hope to finish a prototype soon.

Tnx in advance,

TO