SOLUTION: The demand and supply equations for a certain item are given by: D=-5p+10 S=-p^2+30p-8 Find both possible solutions and determine the equilibrium price This is what I have

Question 98233: The demand and supply equations for a certain item are given by:
D=-5p+10
S=-p^2+30p-8
Find both possible solutions and determine the equilibrium price

This is what I have so far:
-5p+40=-p^2+30p-8
p^2-35p+48=0
p^2-36p=-48 I am now unsure of what to do from here.
Thank you for your help
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
To find the equilibrium, set the equations equal to one another

Get all terms to one side and combine like terms

Let's use the quadratic formula to solve for p:

Starting with the general quadratic

the general solution using the quadratic equation is:

So lets solve ( notice , , and )

Plug in a=1, b=-35, and c=48

Negate -35 to get 35

Square -35 to get 1225 (note: remember when you square -35, you must square the negative as well. This is because .)

Multiply to get

Combine like terms in the radicand (everything under the square root)

Simplify the square root (note: If you need help with simplifying the square root, check out this solver)

Multiply 2 and 1 to get 2

So now the expression breaks down into two parts

or

Now break up the fraction

or

Simplify

or

So these expressions approximate to

or

So our possible solutions are:
or

However, since generates a negative supply and demand, the only solution is
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