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Given 2 circles on a plane, how do you calculate the intersecting points?

In this example I can do the calculation using the equilateral triangles that are described by the intersection and centres of the 2 circles, however, I need a more general formula that will provide the coordinates of the 2 intersection points C and D, on circles that are not placed so conveniently, or of the same radius.

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    Solve the the given 2 equations of the circle. For more you can see these links: - http://paulbourke.net/geometry/circlesphere/ (scroll down) - http://mathworld.wolfram.com/Circle-CircleIntersection.html2011-05-17

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