Find the real solutions, if any, of the following equation. Use the quadratic formula. \( 5 x^{2}=6 x \) Select the correct choice below and, if necessary, fill in the answer box to complete your answer. A. The solution set is \( \} \) (Simplify your answer. Type an exact answer, using radicals as needed. Use a comma to separate answers as needed. Use integers or fractions for any numbers in the expression.) B. The solution is not a real number.

To find the real solutions of the equation \( 5x^{2} = 6x \) using the quadratic formula, follow these steps: 1. **Rewrite the equation in standard form:** \[ 5x^{2} - 6x = 0 \] 2. **Identify the coefficients:** \[ a = 5, \quad b = -6, \quad c = 0 \] 3. **Apply the quadratic formula:** \[ x = \frac{-b \pm \sqrt{b^{2} - 4ac}}{2a} \] 4. **Substitute the coefficients into the formula:** \[ x = \frac{-(-6) \pm \sqrt{(-6)^{2} - 4(5)(0)}}{2(5)} = \frac{6 \pm \sqrt{36}}{10} \] 5. **Simplify under the square root:** \[ \sqrt{36} = 6 \] 6. **Find the two possible solutions:** \[ x = \frac{6 + 6}{10} = \frac{12}{10} = \frac{6}{5} \] \[ x = \frac{6 - 6}{10} = \frac{0}{10} = 0 \] 7. **Write the solution set:** \[ \left\{ 0, \frac{6}{5} \right\} \] **Answer:** **A.** The solution set is \( \left\{ 0, \frac{6}{5} \right\} \)