The expression you provided is a quadratic expression: \(3x^2 - 7x + 9\).

To solve or analyze this expression, we can consider the following steps:

1. **Factoring:** We can attempt to factor the quadratic expression, but in this case, it does not factor nicely over the integers.
  
2. **Using the Quadratic Formula:** The roots of the quadratic equation \(3x^2 - 7x + 9 = 0\) can be found using the quadratic formula:
   \[
   x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
   \]
   where \(a = 3\), \(b = -7\), and \(c = 9\).

3. **Discriminant:** The discriminant \(D = b^2 - 4ac\) determines the nature of the roots:
   \[
   D = (-7)^2 - 4(3)(9) = 49 - 108 = -59
   \]
   Since the discriminant is negative, the roots of the quadratic equation are complex (not real).

Would you like to proceed with solving for the complex roots, or is there another aspect of the expression you'd like to explore?

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Here are some related questions:

1. How do you solve quadratic equations by completing the square?
2. What are the steps to graph a quadratic function?
3. How does the discriminant determine the nature of the roots?
4. Can we use the quadratic formula for non-quadratic equations?
5. What are the real-world applications of quadratic equations?

**Tip:** The discriminant gives you quick insight into the nature of the roots without fully solving the equation.

Explore the quadratic equation 3X² - 7x + 9 with a detailed analysis. Learn about the quadratic formula and how to determine the nature of roots using discriminant. Suitable for students in Grades 10-12.

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