Question 78365
The equilibrium is achieved when the demand = supply
==> -200p + 35,000 = -p^2 + 400p – 20,000

Adding p^2 - 400p + 20000 to both sides we get,

==> p^2 - 400p + 20000 - 200p + 35000 = 0

==> p^2 - 600p + 55000 = 0

==> {{{p =(600+-sqrt(600^2-4*1*55000))/(2*1)}}} 
applying the quadratic formula.

==> {{{p =(600+-sqrt(140000))/(2)}}} 

==> {{{p=(600+-374.2)/(2)}}}

==> p = 112.9 or 487.1

Thus the equilibrium price is 112.9 or 487.1