Profit Maximizing Output: For purely competitive firm, marginal revenue is the present market price, therefore marginal revenue is equivalent to marginal cost when:
P = 26 - (10 * Q) + (0.9 * Q2)
When you know the value of P, you have a quadratic equation with one variable (Q). When you know how to resolve a quadratic equation, you can determine the value of Q which gives the best profit for any specific price.