To find price and equilibrium quantity from a supply and a demand function

[sucksinmath]

Ok, I have a big problem with the following exercise:

In the pair of supply and demand equations below, x represents the quantity demanded in units of a thousand and p the unit price in dollars.p = 80 - 3x² and p = x² + 4x + 32

a) Find the equilibrium quantity (in thousand units).


b) Find the equilibrium price (in dollars)



I think I have to set it up like this: 80 - 3x^{2 =} x² + 4x + 32, and put all the numbers over to the right side and start to solve for zero.. But I have some problems there too, and am not sure if that is the right way to do it either.. Somebody that have a clue?

 

[tkhunny]

You have it! Find 'x' for which p(x) = q(x).

No need to worry about all that "steps" or "stuff over to one side". Just think through what it is you are doing. Strike up an example or two if that will help.

q(x) = 80 - 3x² and p(x) = x² + 4x + 32

So: 80 - 3x² = x² + 4x + 32

Great, now use your inverse properties to rearrange

Add 3x²

80 - 3x² + 3x²= x² + 3x²+ 4x + 32

Simplify

80 = 4x²+ 4x + 32

Keep going!