One of the factories fulfills some order eight days faster than the other. How long can it take for each plant

One of the factories fulfills some order eight days faster than the other. How long can it take for each plant to complete an order, working separately, if it is known that when working together in 24 days, they completed an order 5 times larger.

Let the order volume be 1. The first plant completes the work in x days, the second in x + 8 days. In one day, the first plant fulfills 1 / x part of the order, the second 1 / (x + 8). For 24 days, the factories together perform:

24 / x + 24 / (x + 8) = 5 * 1;

Multiply both sides of the equation by x (x + 8):

24 (x + 8) + 24x = 5x (x + 8);

24x + 192 + 24x = 5x ^ 2 + 40x;

5x ^ 2 + 40x – 48x – 192 = 0;

5x ^ 2 – 8x – 192 = 0;

D = 64 + 4 * 5 * 192 = 3904.

The square root of 3904 is an irrational number, so the equation has no integer solutions. Somewhere in the problem statement an error was made.