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The uploaded image shows a mathematical problem that involves the quadratic formula. Here's the problem extracted from the image:

### Problem:
Solve the quadratic equation using the quadratic formula:
\[
3x^2 + 6x - 9 = 0
\]

### Solution:
The quadratic equation is of the form \(ax^2 + bx + c = 0\), where \(a = 3\), \(b = 6\), and \(c = -9\).

The quadratic formula is given by:
\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\]

Plugging in the values:
\[
x = \frac{-6 \pm \sqrt{6^2 - 4(3)(-9)}}{2(3)}
\]

Simplifying further:
\[
x = \frac{-6 \pm \sqrt{36 + 108}}{6}
\]
\[
x = \frac{-6 \pm \sqrt{144}}{6}
\]
\[
x = \frac{-6 \pm 12}{6}
\]

This gives us two solutions:
1. \(x_1 = \frac{-6 + 12}{6} = 1\)
2. \(x_2 = \frac{-6 - 12}{6} = -3\)

### Final Answer:
The solutions to the quadratic equation \(3x^2 + 6x - 9 = 0\) are \(x = 1\) and \(x = -3\).

Do you want details or have any questions?

Here are 5 related questions:
1. How do you derive the quadratic formula from a standard quadratic equation?
2. Can all quadratic equations be solved using the quadratic formula?
3. What do the solutions represent graphically on the parabola of the equation?
4. How can you determine the nature of the roots (real or imaginary) using the discriminant?
5. How would the solutions change if the quadratic equation was \(3x^2 + 6x + 9 = 0\)?

**Tip:** Always check the discriminant \(b^2 - 4ac\) before solving to determine if the roots are real or complex.

Solve the quadratic equation 3x^2 + 6x - 9 = 0 using the quadratic formula.

This tutorial provides a detailed step-by-step solution to the quadratic equation 3x^2 + 6x - 9 = 0 using the quadratic formula. Ideal for students in Grades 8-10, this guide covers essential algebraic concepts and explains the quadratic formula theorem.

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