To solve the quadratic equation \( 2x^2 - 11x = 6 \), follow these steps:

1. **Rewrite the equation in standard form:**
   \[
   2x^2 - 11x - 6 = 0
   \]

2. **Apply the quadratic formula:**
   The quadratic formula is given by:
   \[
   x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
   \]
   Here, \( a = 2 \), \( b = -11 \), and \( c = -6 \).

3. **Calculate the discriminant:**
   \[
   \Delta = b^2 - 4ac = (-11)^2 - 4(2)(-6) = 121 + 48 = 169
   \]

4. **Find the roots:**
   \[
   x = \frac{-(-11) \pm \sqrt{169}}{2(2)} = \frac{11 \pm 13}{4}
   \]

   This gives two solutions:
   \[
   x_1 = \frac{11 + 13}{4} = \frac{24}{4} = 6
   \]
   \[
   x_2 = \frac{11 - 13}{4} = \frac{-2}{4} = -\frac{1}{2}
   \]

So, the solutions are \( x = 6 \) and \( x = -\frac{1}{2} \).

Would you like further details or have any questions? Here are some related questions you might find interesting:

1. How do you determine the discriminant of a quadratic equation?
2. What do the different values of the discriminant indicate about the nature of the roots?
3. How do you factor a quadratic equation instead of using the quadratic formula?
4. What are some real-world applications of solving quadratic equations?
5. How can you verify the solutions of a quadratic 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 - 11x = 6 with a detailed step-by-step solution. Understand the quadratic formula and calculation of discriminant. Suitable for high school students in Grades 9-12.

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