Question 1124737
{{{36x^2+1875x-6500}}}


Opens upward.  Look for zeros or the break-even points, P(x)=0; solve for x.


Vertex:
x value,  {{{-1875/(2*36)=-1875/72=-625/24}}}



Roots-Zeros

discriminant {{{1875^2+4*36*6500=4451625=3*3*3*5*5*5*1319=9*25*15*1319}}}
-
{{{x=(-1875+3*5*sqrt(15*1319))/72}}}

{{{x=(-625+5*sqrt(19785))/24}}}

x 
is about 3.262.
Only nonzero whole number is allowed.
No profit at 3 units
Any profit begins at 4 units for x.
Profit only increases for any whole number x greater than 4 units.