Question 106117
{{{C=250x^2 - 24000}}}
{{{R=200x - 1000}}}
Find x when C=R?
{{{C=R}}}
{{{250x^2-24000=200x-1000}}}
{{{250x^2-200x-23000=0}}}
Use the quadratic formula,
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
{{{x = (-(-200) +- sqrt( (-200)^2-4*250*(-23000) ))/(2*250) }}}
{{{x = (200 +- sqrt( 23040000 ))/(500) }}}
{{{x = (200 +- (4800))/(500) }}}
Since a negative unit sold doesn't make sense, we'll only calculate the positive value. 
{{{x = (5000)/(500) }}}
{{{x = 10 }}}
10 units is the break-even point.