To solve the quadratic equation \( 2x^2 - 7x + 6 = 0 \), we can use the quadratic formula:

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

In this equation, \( a = 2 \), \( b = -7 \), and \( c = 6 \).

1. **Calculate the discriminant**:

\[
\Delta = b^2 - 4ac = (-7)^2 - 4(2)(6)
\]
\[
\Delta = 49 - 48 = 1
\]

2. **Apply the quadratic formula**:

\[
x = \frac{-(-7) \pm \sqrt{1}}{2(2)}
\]
\[
x = \frac{7 \pm 1}{4}
\]

3. **Find the two solutions**:

\[
x_1 = \frac{7 + 1}{4} = \frac{8}{4} = 2
\]
\[
x_2 = \frac{7 - 1}{4} = \frac{6}{4} = \frac{3}{2}
\]

So, the solutions are:
\[
x = 2 \quad \text{and} \quad x = \frac{3}{2}
\]

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Would you like more details on how the quadratic formula works, or help with any other problems?

Here are some related questions:

1. What would the solutions be if \( a = 1 \), \( b = -7 \), and \( c = 6 \) in a quadratic equation?
2. How can you factorize the quadratic equation instead of using the quadratic formula?
3. How does the discriminant determine the number of solutions for a quadratic equation?
4. Can the quadratic formula be used for non-real solutions? How would that look?
5. What would happen if \( c \) were negative in the given equation?

**Tip:** Always check your solutions by substituting them back into the original equation to ensure they satisfy it.

Learn how to solve the quadratic equation 2x^2 - 7x + 6 step-by-step with detailed solutions. This problem covers key algebraic concepts, including the quadratic formula and discriminant calculation. Suitable for high school students.

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