Given the supply and the demand functions:
[tex]\begin{gathered} \text{Supply}\colon_{}p=q^2+14q-529 \\ \text{Demand}\colon_{}p=311-5q \end{gathered}[/tex]
The market equilibrium point can be calculated by solving the equation Supply = Demand. Then:
[tex]\begin{gathered} q^2+14q-529=311-5q \\ q^2+19q-840=0 \\ (q-21)(q+40)=0 \\ \\ \Rightarrow q=21\text{ or }q=-40 \end{gathered}[/tex]
We take only the positive value, then:
[tex]\begin{gathered} p=311-5\cdot21=206 \\ \text{Equilibrium point}\colon(21,206) \end{gathered}[/tex]
