Intersection of straight line with 3rd order polynomial

Fishing for some advice on finding a solution to finding the intersections of a straight line with a third order polynomial. Does anyone have experience with a problem like this?

So you want
1st order polynomial (straight line) in x = 3rd order polynomial in x
so you need so find the roots of
(3rd order polynomial in x) - (1st order polynomial (straight line) in x) = 0
which is
another 3rd order polynomial in x = 0;
Google for root finding of 3rd order polynomials.

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[Lat: 51.6, Long: -35] -->                 crossing Lat: 51.2193352796549, Long: -30 <--   [Lat: 51.1166666667, Long: -29]
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Intersection of straight line with 3rd order polynomial

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