Question 7 - The Science Project

During a science project, Pedro created a system that is governed by the following equation:

$$f(x)=\frac{1}{32}{x}^{2}a-\frac{1}{2}xz+3$$

In this system, $a$ and $z$ are constants that are adjusted manually by him, while $x$ is the primary variable he wants to change. During his experimental tests, he found that the system can be very unstable, only for a few values of $x$ for different $a$ and $z$ the system becomes stable. Can you help him find an equation that given  $a$ and $z$ he can easily find the value of $x$?

1. $x=\frac{16z}{2a}$
2. $x=\frac{16za}{2}$
3. $x=\frac{2az}{16}$
4. $x=\frac{16a}{2z}$
5. None of the above.

  Original idea by: Pedro Henrique Di Francia Rosso