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) About Me  (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 ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-35x%2B48+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-35%29%5E2-4%2A1%2A48=1033.

Discriminant d=1033 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--35%2B-sqrt%28+1033+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-35%29%2Bsqrt%28+1033+%29%29%2F2%5C1+=+33.5701586799882
x%5B2%5D+=+%28-%28-35%29-sqrt%28+1033+%29%29%2F2%5C1+=+1.4298413200118

Quadratic expression 1x%5E2%2B-35x%2B48 can be factored:
1x%5E2%2B-35x%2B48+=+%28x-33.5701586799882%29%2A%28x-1.4298413200118%29
Again, the answer is: 33.5701586799882, 1.4298413200118. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-35%2Ax%2B48+%29