Let's solve the quadratic equation:

\[
6x^2 - 20 = 0
\]

### Step 1: Simplify the equation
Add 20 to both sides to isolate the term with \(x^2\):

\[
6x^2 = 20
\]

### Step 2: Solve for \(x^2\)
Now divide both sides by 6 to isolate \(x^2\):

\[
x^2 = \frac{20}{6} = \frac{10}{3}
\]

### Step 3: Take the square root of both sides
To solve for \(x\), take the square root of both sides:

\[
x = \pm \sqrt{\frac{10}{3}}
\]

This gives the solutions:

\[
x = \pm \frac{\sqrt{30}}{3}
\]

So the solutions to the equation are:

\[
x = \frac{\sqrt{30}}{3} \quad \text{or} \quad x = -\frac{\sqrt{30}}{3}
\]

Would you like more details on any of these steps or the solution process?

Here are 5 related questions for further practice:
1. Solve \(5x^2 - 15 = 0\).
2. Solve \(7x^2 + 21 = 0\).
3. What are the solutions to \(9x^2 - 36 = 0\)?
4. Simplify and solve \(4x^2 - 28 = 0\).
5. How do you solve \(2x^2 - 8 = 0\)?

**Tip**: When solving quadratic equations, always check if you can simplify the equation by dividing through by common factors before solving for \(x\).

Discover how to solve the quadratic equation 6x^2 - 20 = 0 with a clear step-by-step solution. Learn key algebra concepts like isolating x^2, dividing coefficients, and applying the square root property. Ideal for students in Grades 8-10.

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