In the side wall of the high cylindrical tank at the very bottom, a crane is fixed. after opening it

In the side wall of the high cylindrical tank at the very bottom, a crane is fixed. after opening it, water begins to flow out of the tank. The height of the water column changes according to the law H (t) = 5-16t + 0.128t ^ 2, where t is the time in minutes for how many minutes will the water flow out of the tank?

When the water completely drains out of the tank, then the height of its column will become equal to zero, i.e .:

H (t) = 0,

5 – 16 * t + 0.128 * t² = 0.

Let’s solve by the discriminant formula, we get:

D = 6336/25, √D = 24 * √11 / 5.

Then the roots of the equation will be expressed by numbers:

t1,2 = 125 * (16 ± (24 * √11 / 5)) / 32.

t1 ≈ 0.31 s, t2 ≈ 124.7 s.

Obviously, water could not flow out almost immediately after opening the tap in 0.31 s, so it flowed out in 124.7 s = 2 min 4.7 s.