Finding the intersect between a quadratic and a line

Question

I am trying to find the intersect between a straight line and a quadratic curve, however the result I am getting appears to be imaginary although I don't see how this can be the case as I can see them intersect on real axes:

Import numpy
#quadratic coefficients



a,b,c = (-3.09363812e-04, 1.52138019e+03, -1.87044961e+09)

# y = ax^2 + bx + c



#line coefficients

m,d = (1.06446434e-03, -2.61660911e+03)

#y = mx + d



intersect = (-(b-m)+((b-m)**2 - 4*a*(c-d))**0.5)/(2*a)

print(intersect)

The output of this is 2458883.4674943495-107.95731226786134j

I am trying to find the intersect between the yellow curve over the blue points and the black dotted line

Answer 1

Here's the correct graphs of the parabola and line described in the question. Definitely different from those shown above. As you can see, line and parabola do not intersect.