Question 42812
Price will be in equilibrium when demand is equal to supply.


So for equilibrium price, D = S i.e. {{{-200p + 35000 = -p^2 + 400p - 20000}}}
or {{{p^2 - 600p + 55000 = 0}}}.


To find the equilibrium price we have to solve the above quadratic equation
{{{p^2 - 600p + 55000 = 0}}}.
Applying quadratic formula, 
{{{p = (-(-600) +- sqrt( (-600)^2-4*1*55000 ))/(2*1) }}} 
or {{{p = (600 +- sqrt(360000 - 220000))/2 }}}
or {{{p = (600 +- sqrt(140000))/2 }}}
Either p = 487.08 or p = 112.92


Hence $487.08 and $112.92 are the two values of equilibrium prices.