Answer:
the equilibrium quantity is 6 and the equilibrium price is 112.
Explanation:
The equilibrium quantity and price occur at the point where the supply and demand curves intersect. At this point, the quantity supplied is equal to the quantity demanded, and the price is the equilibrium price.
Setting the supply and demand functions equal to each other, we get:
x²+8x+20 = -x²+4x+100
Simplifying this equation, we get:
2x² - 4x - 80 = 0
Dividing both sides by 2, we get:
x² - 2x - 40 = 0
Factoring this quadratic equation, we get:
(x - 6)(x + 4) = 0
Therefore, the equilibrium quantity is x = 6 or x = -4. However, since we are dealing with a quantity of a commodity, which cannot be negative, we can ignore the solution x = -4.
Substituting x = 6 into either the supply or demand function, we can find the equilibrium price:
p = 6² + 8(6) + 20 = 112
Therefore, the equilibrium quantity is 6 and the equilibrium price is 112.