SOLUTION: P(x)= - 0.08x^2 + 60x - 750 how many units will give a break even point for this product? I'm attempting to use the quadratic equation to solve however I am stuck.

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Question 332126: P(x)= - 0.08x^2 + 60x - 750 how many units will give a break even point for this product? I'm attempting to use the quadratic equation to solve however I am stuck.
Found 2 solutions by ankor@dixie-net.com, josmiceli:
Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
P(x)= - 0.08x^2 + 60x - 750 how many units will give a break even point for this product?
:
Break-even point is when profit is 0, therefore
-.08x^2 + 60x - 750 = 0
using the quadratic formula;
in this problem: a=-.08. b=60, c=-750

:

:

Two solutions, but we want the lowest value here

x =
x = +12.5, ~ 13 units to break even (a slight profit, integer units required)
;
:
Check in the original equation
-.08(13^2) + 60(13) - 750 = +$43.52, a slight profit

Answer by josmiceli(19441) (Show Source):
You can put this solution on YOUR website!
If is
Profit as a function of units, then the break
even point is where there is zero Profit.

Multiply both sides by

You can complete the square also

Multiply both sides by

Take square root of both sides

and

There is a break-even point after 12 units and another
after 737 units
Here's a plot: