It seems there is a typo in the equation you've written. Did you mean:

\[ 3x^2 + 8x + 4 = 0 \]?

If so, this is a quadratic equation. We can solve it using the **quadratic formula**:

\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\]

For the equation \( 3x^2 + 8x + 4 = 0 \), the coefficients are:
- \( a = 3 \)
- \( b = 8 \)
- \( c = 4 \)

Now, let's calculate the discriminant \( \Delta = b^2 - 4ac \) and then solve for \( x \). I'll do the math for you.

\[
\Delta = 8^2 - 4(3)(4) = 64 - 48 = 16
\]

Now, applying the quadratic formula:

\[
x = \frac{-8 \pm \sqrt{16}}{2(3)} = \frac{-8 \pm 4}{6}
\]

So the two solutions are:

\[
x_1 = \frac{-8 + 4}{6} = \frac{-4}{6} = -\frac{2}{3}
\]

\[
x_2 = \frac{-8 - 4}{6} = \frac{-12}{6} = -2
\]

Thus, the solutions are:

\[
x_1 = -\frac{2}{3}, \quad x_2 = -2
\]

Would you like more details, or do you have any questions?

Here are 5 related questions you might want to explore:

1. How do we know when to use the quadratic formula?
2. What does the discriminant tell us about the nature of the solutions?
3. Can quadratic equations always be solved using factoring instead of the quadratic formula?
4. How can we graph the quadratic function \( y = 3x^2 + 8x + 4 \)?
5. What are some real-life applications of quadratic equations?

**Tip:** Always check the discriminant before applying the quadratic formula to see if the equation has real or complex solutions!

Learn how to solve the quadratic equation 3x^2 + 8x + 4 = 0 using the quadratic formula. This detailed guide covers essential algebraic concepts, such as the discriminant and the quadratic formula. Suitable for students in Grades 8-10.

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