3x²-8x-3=0 Solve each equation by factoring or using quadratic formula 

To solve the quadratic equation \( 3x^2 - 8x - 3 = 0 \), we will use the **quadratic formula**, which is:

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

Where \( a = 3 \), \( b = -8 \), and \( c = -3 \).

### Step-by-step solution:

1. **Calculate the discriminant**:
   \[
   \Delta = b^2 - 4ac = (-8)^2 - 4(3)(-3) = 64 + 36 = 100
   \]

2. **Apply the quadratic formula**:
   \[
   x = \frac{-(-8) \pm \sqrt{100}}{2(3)} = \frac{8 \pm 10}{6}
   \]

3. **Find the two solutions**:
   \[
   x_1 = \frac{8 + 10}{6} = \frac{18}{6} = 3
   \]
   \[
   x_2 = \frac{8 - 10}{6} = \frac{-2}{6} = -\frac{1}{3}
   \]

### Final Answer:
The solutions are:
\[
x = 3 \quad \text{or} \quad x = -\frac{1}{3}
\]

Would you like further details or have any questions?

Here are 5 related questions:
1. How do you determine if factoring is possible before using the quadratic formula?
2. What does the discriminant tell us about the number of solutions?
3. Can you factor the equation \(3x^2 - 8x - 3 = 0\) directly?
4. What is the significance of the discriminant being a perfect square?
5. How does the quadratic formula apply to complex roots?

**Tip**: Always check if the discriminant is positive, zero, or negative to determine the nature of the solutions (real or complex).

3x²-8x-3=0 Solve each equation by factoring or using quadratic formula

Learn how to solve the quadratic equation 3x²-8x-3=0 using the quadratic formula. This step-by-step solution explains key algebraic concepts such as the discriminant and its role in finding the roots of the equation. Ideal for students in Grades 9-10.

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