g = 9.81 # acceleration due to gravity
y_0 = 1.5 # initial height
v_0 = 12.8 # initial velocity
t = 2
print("y =", y_0 + v_0 * t - 0.5 * g * t**2)
y_1 = 5
# equation for t
# y_1 = y_0 + v_0 * t - 0.5 * g * t**2
# equation rearranged
# (0.5 * g) * t**2 - v_0 * t + (y_1 - y_0) = 0
# a t^2 + b t + c = 0
a = 0.5 * g
b = -v_0
c = y_1 - y_0
disc = b**2 - 4*a*c
t_1 = (-b - disc**0.5)/(2*a)
t_2 = (-b + disc**0.5)/(2*a)
print(t_1, t_2)
y = 7.48
0.31034543701622325 2.29923662210712