Need calculus help: A product can be produced at total cost

[Rebel*and*Saint]

A product can be produced at a total cost C(x) = 800 + 100x^2 + x^3 where x is the number of units produced (x>0). The total revenue for the same product is given by R(x) = 60000x - 50x^2

a) What are the production levels (number of units) for which the company actually makes a profit?

b) Determine the number of units that have to be produced to maximize the profit.

Thus far I have done this--

Profit = revenue - costs

cost C(x) = 800 + 100x^2 + x^3

(x>0)

Revenue R(x) = 60000x + 50x^2

I can't seem to get past this point, and any help is greatly appreciated!
Thank you

 

[galactus]

R-C=P

\(\displaystyle \L\\\underbrace{60000x-50x^{2}}_{\text{R(x)}}-\underbrace{(800+100x^{2}+x^{3})}_{\text{C(x)}}=\underbrace{{-}x^{3}-150x^{2}+600000x-800}_{\text{P(x)}}\)

To find max profit, differentiate P(x), set to 0 and solve for x.