Post Closed as "off topic" by Harry Gindi, Reid Barton, Steve Huntsman, Harald Hanche-Olsen, Ryan Budney

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How to solve a bivariate quadratic equation?

I have an equation: Ax² + By² + 2Cxy + 2Dx + 2Ey + F = P

A,B,C,D,E,F and P are constants.

Now I'd need to find out the solutions in range: x+y <= 1 and x >= 0, y >= 0.

How to solve it?

(I can solve a ray intersection with quadratic bezier triangle by using the solution of this equation)