Question 953448
equilibrium: the price and quantity that correspond to the point where supply and demand intersect (where Demand= Supply)

Demand: {{{p=840-12q}}} {{{Supply=7q^2+2q}}}

{{{7q^2+2q=840-12q}}}

{{{7q^2+2q-840+12q=0}}}

{{{7q^2+14q-840=0}}}

{{{7q^2/7+14q/7-840/7=0}}}

{{{q^2+2q-120=0}}}

{{{q^2+12q-10q-120=0}}}

{{{(q^2+12q)-(10q+120)=0}}}

{{{q(q+12)-10(q+12)=0}}}

{{{(q-10)(q+12) = 0}}}

solutions:

if {{{(q-10) = 0}}}=>{{{q=10}}}

if {{{(q+12) = 0}}}=>{{{q=-12}}}...disregard this solution, the quantity cannot be negative

so, your solution is:{{{q=10}}}-----quantity

now find {{{p}}}

 {{{p=840-12q}}}

 {{{p=840-12*10}}}

 {{{p=840-120}}}

 {{{p=720}}}--------price

intersection point is at ({{{q}}},{{{p}}})=({{{10}}},{{{720}}})