When we know the mathematical form of the demand and supply relationships, we can give quantitative answers, and we can also confirm that our qualitative answers are correct. Suppose we have the following demand and supply relationships:
       Demand: Q_D = 120 - 2P
       Supply: Q_S = -30 + P

We learned that we can find the equilibrium price and quantity by equating them and solving for the price.
        120 - 2P = -30 + P
        150 = 3P
        P = 50
        Q = 20

Now, suppose demand shifts out so that the new demand relationship is:
        Q_D2 = 180 - 2P

We can solve for the new equilibrium:
        180 - 2P = -30 + P
        210 = 3P
        P = 70
        Q = 40

Our quantitative answer confirms the qualitative result of our graphical analysis. When demand shifts out, both equilibrium price and quantity increase.