1st Post: find price, quantity that give equilibrium

[darkskinned]

If the supply and demand functions for a certain product are given by the equations 2p – q + 6 = 0 and (p + q(q + 10) = 3696, respectively, find the price and quantity that give market equilibrium.

So far this is what I have done:

. . .q^2 + p + 10 = 3696 = q^2 + p - 3686 = 0

. . .2p – q + 6 = q^2 + p - 3686

. . .q^2 – p – 3680 = 0

Any help would be appreciated.

 

[pka]

\(\displaystyle \L
\begin{array}{l}
p + q(q + 10) = 3696\quad \Rightarrow \quad q^2 + 10q + p = 3696\quad \Rightarrow \quad p = 3696 - 10q - q^2 \\
\\\
2p - q + 6 = 0\quad \Rightarrow \quad p = \frac{1}{2}q - 3 \\
\end{array}\)

 

[darkskinned]

Thank you. Do I combined these to get the final equation that finds the price and quantity that gives market equilibrium?

 

[Denis]

Yes. First, multiply by 2 to get rid of q/2 fraction:
q - 6 = 7392 - 20q - 2q^2
2q^2 + 21q - 7398 = 0 : all yours to finish!