You don't need to solve it for D = 0 nor for D < 0

You would need to solve for D = 0 if the line intersects the parabola at only one place.
You would need to solve for D < 0 if the line doesn't intersect the parabola.

In our scenario,
If b > -7/3, the line intersects the parabola at two places
If b = -7/3, the line intersects the parabola at exactly one place
If b < -7/3, the line doesn't intersect the parabola.