Projectile Motion Time Of Flight Proof

Modelling a $d=-4.9(t^2)+v\sin (t)$ curve, we see that there are 2 roots. One is always 0, the other root, is the total time of flight. We know that this point corresponds to -b/2a, and that this point is always 50% of the total flight time. Since the left root is always 0, we know that -b/2a will always be half of the total flight time.