That's not an equation. You need to have an equals sign somewhere.
I have an equation 2x - 4 + (24/x^2) and I am struggling to isolate x because I end up with two separate x. Would anyone be willing to help clear up the confusion. Its pretty obvious my math skills are not the greatest and I cannot seem to get this right.
$$2x -4 + \frac{24}{x^2}=0$$
multiply both sides by x^{2}
$$2x^3 - 4x^2 + 24 = 0$$
equations that have x^{3} in them in general aren't so easy to solve and indeed the solutions to this equation are something of a mess.
The one real solution this equation (the other two are complex numbers) is approximately x = -1.78141
There would be no easy way for you to find this by hand.
Please see romsek's response. However, you have not told us how this equation arose. Problems in a text usually have fairly "nice" answers, not messes. Are you sure that this equation is correct? (If this equation arose from real life rather than a text or class, please pay no attention to this post: real life is often messy.)
The Cost function is C = q^3 - 4q^2 + 24q. The only other thing I was given was the demand function= 120 - 3p. I am having trouble deriving the supply function from the cost function. Once I have the supply function I can get the equilibrium price and quantity no problem. My comprehension of Econ is mostly conceptual. The math is now and has always given me fits.
$total\ cost = q^3 - 4q^2 + 24q,\ q \ge 0.$ Is this correct?
If so, $average\ cost\ (if\ q > 0)\ = \dfrac{q^3 - 4q^2 + 24q}{q} = q^2 - 4q + 24.$
Yes, that is average cost, but I need to derive a supply function from cost in order to find the equilibrium. Finding the supply function is what is really giving me trouble. I thought I needed to find q first in order to get price which would allow me to find the supply functino though I may be making more work for myself.
The question keeps changing. First, it was to solve an equation, but the equation given does not appear to be properly derived from the problem.
Second, I am lost by your question about the relevance of a long-term supply function. How can I or anyone determine if it is relevant if we do not know, completely and exactly, what the original problem is? I appreciate that you are trying to show the results of your work and indicating where you have questions. Those are good things to do. But it ranges from difficult to impossible to answer questions if we do not know the complete and exact problem being posed.
The OP SEEMS to be asking about long-term equilibrium, which, assuming perfect competition, occurs when price equals the minimum of long-term average cost and, in the absence of economies or dis-economies of scale or competitive imperfections, price is supply determined and quantity is demand determined. I really have no idea how to proceed because we are guessing about the problem is.
I was not originally asking about the problem as a whole, just the math leading up to it. I was not even asking the right question because what I was trying to do was not required. I apologize about not being direct in the first place, I was just trying to do most of the problem myself. All I originally wanted help with was finding q which I did not need to do. I appreciate all the help, because it is what has led me to knowing how to set this problem up correctly (i.e. setting the derivative of the cost function equal to the demand function to find the equilibrium). Calculus and math in general are not my strong suit, so sorry about all the confusion.