Problem #6654 Work out the equilibrium?Given the supply and demand functions, determine the equilibrium price and quantity. $P=Qs^{2}+11Qs+75$ $P=-Qd+103$ $Q=P=$.

Solution First, set $Qs$ (quantity supplied) equal to $Qd$ (quantity demanded). Denote by $Q$ their common value. So, $Q^{2}+11Q+75=-Q+103$, $Q^{2}+12Q-28=0$, thus $Q=2$ and, hence, $P=-2+103=101$.

Answer $Q=2$, $P=101$.