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 $x(x+5) = -n$? Express your answer as a common fraction

Using the discriminant, the possible values of n are 5, 6, 7, 8, 9, 10, so the probability is 6/10 = 3/5.

Good logic guest but you need to be very careful to read the question properly and answer what is asked.