We need to solve the equation $\frac{25}{3x} = \frac{3x}{9}$ for $x$.

1. Problem Description

We need to solve the equation $\frac{25}{3x} = \frac{3x}{9}$ for $x$.

2. Solution Steps

First, we cross-multiply to get rid of the fractions:

$$25 \cdot 9 = 3x \cdot 3x$$

$$225 = 9x^2$$

Now, divide both sides by 9:

$$\frac{225}{9} = x^2$$

$$25 = x^2$$

Take the square root of both sides:

$$x = \pm \sqrt{25}$$

$$x = \pm 5$$

3. Final Answer

$x = \pm 5$