If I assume you meant supply is determined as [q_(s)=3p^2-4p] and demand is determined as [q_(d)=-p^2+24] then I would calculate that the equilibrium is where [q_(s)=q_(d)] and p>0. So I set up the equation [3p^2-4p=-p^2+24] I add [p^2] to both sides of the equation yielding [4p^2- 4p=24] I subtract 24 from each side, yielding the quadratic equation [4p^2-4p-24=0] I factor the equation [(2p-6)(2p+4)=0] so that means [2p-6=0] or [2p+4=0] In the former case 2p=6 so p=3, and in the latter 2p=-4 so p=-2. The economic nature of the question requires p>0, so [p!=-2] and thus the equilibrium price is $3.00 each. Then to determine the equilibrium quantity, we solve either q expression for p=3. [q_(s)=3(3)^2-4(3)=3(9)-12=27-12=15] [q_(d)=-(3^2)+24=-9+24=15] So the equilibrium quantity is 15 items. The price and quantity for market equilibrium is 15 items at $3.00 each. Solution If I assume you meant supply is determined as [q_(s)=3p^2-4p] and demand is determined as [q_(d)=-p^2+24] then I would calculate that the equilibrium is where [q_(s)=q_(d)] and p>0. So I set up the equation [3p^2-4p=-p^2+24] I add [p^2] to both sides of the equation yielding [4p^2- 4p=24] I subtract 24 from each side, yielding the quadratic equation [4p^2-4p-24=0] I factor the equation [(2p-6)(2p+4)=0] so that means [2p-6=0] or [2p+4=0] In the former case 2p=6 so p=3, and in the latter 2p=-4 so p=-2. The economic nature of the question requires p>0, so [p!=-2] and thus the equilibrium price is $3.00 each. Then to determine the equilibrium quantity, we solve either q expression for p=3. [q_(s)=3(3)^2-4(3)=3(9)-12=27-12=15] [q_(d)=-(3^2)+24=-9+24=15] So the equilibrium quantity is 15 items. The price and quantity for market equilibrium is 15 items at $3.00 each..