Question 104076
The demand and supply equations for a certain item are given by
    D = –5p + 40
    S = –p^2 + 30p – 8
Find the equilibrium price
Equilibrium is when supply = demand;
{{{-5p+40=-p^2+30p-8}}}
{{{p^2-5p-30p+40+8=0}}}
{{{p^2-35p+48=0}}}
Use quadratic equation to solve;
{{{(35+-sqrt(35^2-4(1)(48)))/2(1)}}}
{{{(35+-sqrt(1225-192))/2}}}
{{{(35+-sqrt(1033))/2}}}

Now we two equations to solve, because we have 35+ and 35-;
{{{P=(35+32.14)/2}}}
P=33.57
{{{P=(35-32.14)/2}}}
{{{P=2.86/2}}}
P=1.43
:)