To solve the quadratic equation \( 2t^2 + 7t + 6 = 0 \), we can apply the **quadratic formula**:

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

For the equation \( 2t^2 + 7t + 6 = 0 \), the coefficients are:
- \( a = 2 \)
- \( b = 7 \)
- \( c = 6 \)

Let's substitute these into the quadratic formula:

\[
t = \frac{-7 \pm \sqrt{7^2 - 4(2)(6)}}{2(2)}
\]

Simplifying step by step:

1. Calculate the discriminant:
   \[
   \Delta = 7^2 - 4(2)(6) = 49 - 48 = 1
   \]

2. Substitute the discriminant back into the formula:
   \[
   t = \frac{-7 \pm \sqrt{1}}{4}
   \]

3. Solve for the two possible values of \( t \):
   \[
   t_1 = \frac{-7 + 1}{4} = \frac{-6}{4} = -\frac{3}{2}
   \]
   \[
   t_2 = \frac{-7 - 1}{4} = \frac{-8}{4} = -2
   \]

Therefore, the solutions are:
\[
t = -\frac{3}{2} \quad \text{or} \quad t = -2
\]

Would you like more details on any part of this solution?

Here are 5 related questions to consider:
1. How do you check if the solutions to a quadratic equation are correct?
2. What happens if the discriminant is negative?
3. Can you factor the equation \( 2t^2 + 7t + 6 = 0 \) instead of using the quadratic formula?
4. What are real-life applications of quadratic equations?
5. How would the graph of \( 2t^2 + 7t + 6 \) look like?

**Tip:** Always check the discriminant \( b^2 - 4ac \) first to determine the nature of the solutions!

Discover how to solve the quadratic equation 2t^2 + 7t + 6 = 0 with a detailed step-by-step solution using the quadratic formula. This guide explains core algebra concepts, including calculating the discriminant, and is suitable for students in Grades 8-10.

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