SOLUTION: The demand and supply equations for a certain item are given by D = -5p + 40 S = -p^2 + 30p - 8 Find the equilibrium price.

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Question 42640: The demand and supply equations for a certain item are given by
D = -5p + 40
S = -p^2 + 30p - 8
Find the equilibrium price.
Answer by Nate(3500)   (Show Source): You can put this solution on YOUR website!
Define as total payment:

also known as

and

also known as

Combine:
while you know that


Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=1033 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 1.4298413200118, 33.5701586799882. Here's your graph:
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