Answer: 10 hours
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The break even point occurs when R(h) = C(h). In other words, when the revenue is the same as the cost.
R(h) = C(h)
20+45h = 5h^2-30
20+45h-20 = 5h^2-30-20
45h = 5h^2-50
45h-45h = 5h^2-50-45h
0 = 5h^2-45h-50
5h^2-45h-50 = 0
5(h^2-9h-10) = 0
5(h-10)(h+1) = 0
h-10=0 or h+1=0
h=10 or h=-1
Ignore the negative h value. Negative hours make no sense.
The only practical solution is h = 10
Therefore the break even point occurs when h = 10
