SOLUTION: The demand and supply equations for a certain item are given by D = –5p + 40 S = –p2 + 30p – 8 Find the equilibrium price.

The demand and supply equations for a certain 
item are given by
D = –5p + 40
S = –p2 + 30p – 8
Find the equilibrium price.

The equilibrium price is the price when 

1. no item in the store remains unsold.

and at the same time

2. no customer wants to buy one and can't
   because when they try to buy one at the 
   store they find the store is sold out.

This can only happen when Demand and Supply
are equal. So we set D = S

            D = S
     –5p + 40 = –p² + 30p – 8
p² - 35p + 48 = 0

Can you solve that by the quadratic formula?
If not post again asking how.  Assuming you
can do that, you get two answers

One is when the price is $1.43 (rounded to the nearest penny).
One is when the price is $33.57 (rounded to the nearest penny).

However, we must check these to see if they both are feasible.

Checking the first answer:

D = –5p + 40 = -5(1.43) + 40 = 32.85
S = –p2 + 30p – 8 = -(1.43)² + 30(1.43) - 8 = 32.8551 

That's feasible.

Checking the second answer:

D = –5p + 40 = -5(33.57) + 40 = -127.85
S = –p2 + 30p – 8 = -(33.57)² + 30(33.57) - 8 = -127.8449

We must discard this one because we cannot have a negative
demand or supply.

So the answer is $1.49

Edwin