Question 1154482


Supply:
{{{ p=q^2+20q}}}  
Demand: 
{{{p=-2q^2+10q+5200}}}

The equilibrium is when supply=demand

{{{ q^2+20q=-2q^2+10q+5200}}} 

{{{ q^2+20q+2q^2-10q-5200=0}}} 

{{{ 3q^2+10q-5200=0}}} 

{{{ 3q^2+10q-5200=0}}} ...factor

{{{ 3q^2-120q +130q-5200=0}}}

{{{ (3q^2-120q)+(130q-5200)=0}}}

{{{ 3q(q-40)+130(q-40)=0}}}

{{{(q - 40) (3q + 130) = 0}}}-> we need only positive solution

so, {{{q=40}}}


The equilibrium quantity is {{{q=40}}}.