Revenue is given by f(x) = -15x^2 - 30x + 200
Cost is given by y = 5x - 12
to break even, then Revenue = Cost
Then:

Now, let's solve for x, which is the price
Step #1.
add 12 to both sides

#2
Simplify

#3
subtract 5x from both sides

#4
Simplify

#5
Use the general formula to solve quadratic equation
![x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a};a^2x+bx+c=0](https://img.qammunity.org/2023/formulas/mathematics/college/w2zny7h6q7aj5h414rad9kt0amyjs3cx2w.png)

#6

#7

#8
in decimal numbers

a negative value does not make sense in this case, therefore the answer is
d) $2.77