I choose a random integer n between 1 and 10 inclusive. What is the probability that for the n I chose, there exist no real solutions to the equation x(x + 1) = n ? Express your answer as a common fraction.

There are only 2 integers for n that give solution to the equation:

And that is when n = 2 and n = 6

Therefore, the probability that your n has no solution is: 8 / 10 = 4 / 5