I've previously solved for the following items, but now I'm stuck on how to determine the profit-maximizing price and quantity.(Since MC is in terms of Q2, solving with calculus and algebra can be messy unless you know the quadratic formula. Your table should give an exact answer.)

P = - Q + 90 TC = 0.01Q^3 - 1.4Q^2 + 90Q + 2000 TR = -Q^2 + 90Q MR = -2Q + 90 ATC = 0.01Q^2 - 1.4Q + 90 + 2000/Q TVC = 0.01Q^3 - 1.4Q^2 + 90Q AVC = 0.01Q^2 - 1.4Q + 90 TC = 0.01Q^3 - 1.4Q^2 + 90Q + 2000 MC = 0.03Q^2 - 2.8Q + 90

Q P TC 0 $90 $2,000 10 $88 $2,770 20 $86 $3,320 30 $84 $3,710 40 $82 $4,000 50 $80 $4,250 60 $78 $4,520 70 $76 $4,870 80 $74 $5,360 90 $72 $6,050 100 $70 $7,000

I'm sure I need to use this formula: P = - Q + 90

Where do I start?