Solving for equilibrium with Qs and Qd

This post goes over an example of solving for equilibrium price and quantity using the method detailed in the prior equilibrium solving method post. In this example we are given a Qs equation as shown:

Qs= -7909.88 + 79.0988P

Note that this gives us a positive sloping supply curve and that price has to be at least 100 in order for the supplier to produce anything at all (we can figure this out by dividing the intercept 7909.88 by the coefficient on the price 79.0988).

The next step is exploring the demand equation. In this example we are given a demand function as follows:

Qd= 38650 - 40P

Here we have a downward sloping demand curve and the quantity demanded at a price of 0 will be 38650. Once the price reaches 966.25 we will see a quantity demanded of 0 (found by dividing 38650 by 40).

In order to solve for the equilibrium price and quantity, we will set the two equations equal to each other. This works because we are trying to mathematically find the equilibrium point on the graph where price and quantity are equal (hence setting Qs=Qd).

So:
Qs=Qd

leaves us with

-7909.88 + 79.0988P = 38650 - 40P

we should add 7909.88 and 40P to both sides which will leave our unknown variable P on only one side of the equation. This leaves us with:

119.0988P = 46559.88

We then divide both sides by 119.0988 in order to find the equilibrium value for P. This results in:

P = 390.9345

We can check this answer by plugging in this value for P into our original demand and supply equations. If our Qs and Qd are the same then we know we did the math right.  When we plug this value for P into our demand equation of:

Qd= 38650 - 40P

We get a Qd of 23012.62

and when we plug in our equilibrium P value into our supply equation of:

Qs= -7909.88 + 79.0988P

We get a Qs of 23012.57

Which is very close and are not entirely equal because of my rounding of the equilibrium price before.