SOLUTION: Could you help me with this problem? The demand and supply equations for a certain item are given by D= -15p + 30 S= -p^2 + 20p - 18 Find the equilibrim price. I

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Question 105207: Could you help me with this problem?
The demand and supply equations for a certain item are given by
D= -15p + 30
S= -p^2 + 20p - 18
Find the equilibrim price.
I have gotten serveral different answers however is the answer $1.43?
Answer by edjones(8007)   (Show Source): You can put this solution on YOUR website!
-15p+30=-p^2+20p-18 Equilibrium exists when supply equals demand.
p^2-35p+48=0 Subtract the right side from the left.
P=1.43, p=33.57
See below.
Ed
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
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: 33.5701586799882, 1.4298413200118. Here's your graph:
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