When you solve for d(profit)/d(price)=0 for price,
you will probably get an equation you don't
know how to solve algebraically, not even
with the quadratic formula. What you should do
in a situation like this is use a "solve" command
or similar on your calculator to get a numerical
estimate of the solution.
If you don't own a calculator with the above
capability, I recommend buying one, and using
sites like wolframalpha.com in the meanwhile:
http://www.wolframalpha.com/input/?i=5*x^3%2Bx^2%2B8*sqrt%28x%29%3D%3D170
P.S. Homeworks 9 through 12 are due on the Tuesday
after spring break. You will enjoy your break more if you
start the homeworks early.
(But also study for the test on March 3!)