Roots of a quadratic can be found with the equation (-b +/- sqrt(b^2-4ac))/2a
where a,b and c are the constants in ax^2+bx+c=0.

sqrt() functions may barf on negative numbers (or incorrectly/misleadingly ignore the sign) so check b^2 >= 4ac; if it isn't then the roots are imaginary, e.g. x^2+1=0 has no real solution; the solutions are +i and -i.