To solve the equation \( 6x^2 = 120 \), follow these steps:

1. **Isolate the \( x^2 \) term:**
   \[
   x^2 = \frac{120}{6} = 20
   \]

2. **Take the square root of both sides:**
   \[
   x = \pm \sqrt{20}
   \]

3. **Simplify the square root:**
   \[
   x = \pm \sqrt{4 \times 5} = \pm 2\sqrt{5}
   \]

So, the solutions are \( x = 2\sqrt{5} \) and \( x = -2\sqrt{5} \).

Would you like further details or have any questions? Here are some related questions you might find interesting:

1. How do you simplify square roots involving products?
2. What are the steps for solving quadratic equations by factoring?
3. How can you solve quadratic equations using the completing the square method?
4. What is the significance of the positive and negative roots in real-world scenarios?
5. How can you approximate square roots to a decimal?

**Tip:** Remember that the square root function has both a positive and negative root when solving quadratic equations.

Learn how to solve the equation 6x^2 = 120 with a detailed step-by-step solution. This problem involves quadratic equations and square roots, covering the quadratic equation formula and properties of square roots. Suitable for students in Grades 9-12.

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