Find the equilibrium quantity and equilibrium price for the commodity whose supply and demand functions are given. supply: p equals q squared plus 20 qp=q2+20q    demand: p equals negative 4 q squared plus 10 q plus 18 comma 600p=−4q2+10q+18,600 the equilibrium quantity is q= ?

Rewriting the two equations:

[Supply] 
[Demand] 

Equilibrium price is when 
Supply = Demand


 ⇒ Simplifying the equation by dividing each term by 5



The simplified equation is in quadratic form.
There are three main methods for solving a quadratic equation: factorizing, completing the square, or quadratic formula. 

Using the formula, we need the value of a, b, and c which are the constant of quadratic equation. 
, and


We have a = 1, b = -2, and c = -3716
Substituting these values into the formula we have



Since 'q' represented quantity, we can't have negative values, so we choose the value of 'q' to be 61.97 ≈ 62 (rounded to the nearest whole number)

Equilibrium quantity = 62