Question 818234
Your start is right, you must have made some calculation error.
If supply is {{{3p-200}}} and demand is {{{3200/p}}}
{{{3200/p = 3p-200}}} is the right equation to make supply equal demand.
Also, from {{{3200/p = 3p-200}}} you get {{{3200=3p^2-200p}}}
and {{{3p^2-200p-3200=0}}} as you meant to write.
 
I see 3 ways to solve that equation:
factoring, completing the square, and using the quadratic formula.
Since I had my calculator next to me,
I found it easier to use the quadratic formula,
which says that the solutions to {{{ax^2+bx+c=0}}} can be calculated as
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
In your case, {{{a=3}}} , {{{b=-200}}} , and {{{c=-3200}}} , so
{{{x = (200 +- sqrt(200^2-4*3*(-3200)))/(2*3) }}}
{{{x = (200 +- sqrt(40000-38400)))/6}}}
{{{x = (200 +- sqrt(78400)))/6}}}
{{{x = (200 +- 280))/6}}}
The solution with the minus sign, {{{x=(200-280)/6=-80/6=-40/3}}}
does not make sense, because the price has to be a positive number of cents.
The other solution is
{{{x=(200+280)/6=480/6=80}}} ,
meaning that pricing each muffin at 80 cents will make supply meet demand.