We have that the demand equation for a certain product is given by:

where x is the number of units produced. Also, that the total revenue is:

And we want to determine prices P that would yield a revenue of 7280 dollars. This means that we want to find values x such that the following equation holds:

We will solve the equation by the quadratic formula. First, we will use the distributive property and we clear out the left side of the equation, to obtain:

In this equation:

And thus, replacing on the quadratic formula we obtain:
![\begin{gathered} x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ =\frac{-132\pm\sqrt[]{(132)^2-4(-0.025)(-7280)}}{2(-0.025)} \\ =\frac{-132\pm\sqrt[]{17424-728}}{-0.05} \\ =\frac{-132\pm\sqrt[]{16696}}{-0.05} \\ \approx(-132\pm129.21)/(-0.05) \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/m2r3jiorq1frvaesqnvfie9aepdntzajt2.png)
Now, for the two solutions, we separate them with the signs + and -.

And for the other one:

This means that the lowest of the prices should be 56 dollars, and the highest price 5224 dollars.