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A piece of equipment has cost function C(x)=50x^2 + 1000 and its revenue

function is R(x)= 500x - x^2, where x is in thousands of items. What is the
least number of items that must be sold in order to break even?

50x^2 + 1000 = 500x - x^2
50x^2 + x^2 + 500= 0
51x^2 + 500 = 0

Do I just do -b/2a = -500/102= -250/51? What do I do next?

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2 answers
  1. well, you should see right off that since 51x^2 is always positive, you can never have 51x^2 = -500.

    So, let's see what happened.

    50x^2 + 1000 = 500x - x^2
    51x^2 - 500x + 1000 = 0

    Now just use the quadratic formula to find the roots.

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  2. wow that was a silly mistake I didn't see the x next to 500 and thought I could just subtract it from 1000

    thank you!

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