please help me with this

Question

Saini sprinkler company installs irrigation systems. To track monthly costs C and revenues R, they use the following functions, where x is the number of systems they install: R (x) = 8x^2 + 2x - 9 C (x) = 7x^2 + 5x - 5 The monthly profit can be found by subtracting cost from revenue: p (x) = R (x) - C (x) Use these equations to find the number of systems to install in order to break-even. (profit equals 0)

Answer 1

R(x)=8x²+2x-9

C(x)=7x²+5x-5

P(x)=R(x)-C(x)=x²-3x-4=0 at break-even.

x²-3x-4=(x-4)(x+1)=0, therefore x=4 (R(4)=C(4)=127).

They would need to install 4 systems to break even.