Question 332126
If {{{P(x)}}} is
Profit as a function of {{{x}}} units, then the break
even point is where there is zero Profit.
{{{P(x)= - 0.08x^2 + 60x - 750}}}
{{{0 = - 0.08x^2 + 60x - 750}}}
Multiply both sides by {{{100/8}}}
{{{0 = -x^2 + 750x - 9375}}}
You can complete the square also
{{{-x^2 + 750x = 9375}}}
Multiply both sides by {{{-1}}}
{{{x^2 - 750x = - 9375}}}
{{{x^2 - 750x + (750/2)^2 = (750/2)^2 - 9375}}}
{{{x^2 - 750x + 375^2 = 375^2 - 9375}}}
{{{(x - 375)^2 = 140625 - 9375}}}
{{{(x - 375)^2 = 131250}}}
Take square root of both sides
{{{x - 375 = 362.284}}}
{{{x = 737.284}}}
and
{{{x - 375 = -362.284}}}
{{{x = 12.716}}}
There is a break-even point after 12 units and another 
after 737 units
Here's a plot:
{{{ graph( 700, 700, -300, 1000, -3000, 12000,  -(8/100)*x^2 + 60x - 750 ) }}}