The boat goes upstream of the river to its destination 120 km and after a short stay returns to the point

The boat goes upstream of the river to its destination 120 km and after a short stay returns to the point of departure. Find the speed of the boat in still water, if the current speed is 3 km / h, the stay lasts 20 minutes, and the boat returns to the point of departure 17 hours after leaving it.

Let’s designate: x km / h – speed of a boat in still water. Therefore, the speed downstream is x + 3 km / h, upstream is equal to x – 3 km / h. 20 minutes is 1/3 hour.
According to the condition of the problem, an equation was drawn up:
120 / (x – 3) + 120 / (x + 3) + 1/3 = 17;

(120 * (x + 3) + 120 * (x – 3)) / (x2 – 9) = 17 – 1/3;

(120x + 360 + 120x – 360) / (x2 – 9) = 50/3;

240x / (x2 – 9) = 50/3;

50x ^ 2 – 450 = 720x;

50x ^ 2 – 720x – 450 = 0;

Discriminant = (-720) * (-720) – 4 * 50 * (-450) = 608400 (the root of 6084 is 780)

x = (720 + 780) / 100 or x = (720 – 780) / 100

x = 15 or x = -0.6

Since the speed cannot be negative, it is equal to 15 km / h.

Answer: the speed of the boat in still water is 15 km / h.