What is the largest positive integer value of $m$ such that the equation $$3x^2 - mx + 7 = 0$$has no real solutions?

For this case we have the following polynomial:

The polynomial has no real solutions when it is met:

Substituting values we have:

Rewriting we have:

Clearing the value of m we have:

Then, the value of the largest positive integer for which the equation has no real solution is:

The largest positive integer value of that is the equation has no real solutions is:

the revenue of the fitness center, y, is the product of two factors: the number of members and the fee paid by each member. there are 320 members now, but number of members goes down by 10 for each $5 increase in fees, so if x is the number of $5 price increases then members is equal to (320 - 10x). since the fee is currently $45, and the fee increases by $5 for every price bump x, the fee is given by (45 + 5x). so, revenue y is given by y = (320 - 10x)(45 + 5x).