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 solve the equation \( 5x^{2} = 6x \), we first rearrange it into standard form as \( 5x^{2} - 6x = 0 \). Next, we can factor out \( x \) to get \( x(5x - 6) = 0 \). This gives us two equations: \( x = 0 \) and \( 5x - 6 = 0 \). Solving \( 5x - 6 = 0 \) yields \( x = \frac{6}{5} \). Thus, the solution set is \( \{ 0, \frac{6}{5} \} \). For a fun fact: Did you know that quadratic equations can have at most two solutions because they are represented by parabolas, which can intersect the x-axis in up to two points? Imagine a roller coaster track that, depending on how high or low you go, might touch the ground at zero, one, or two places! If you're solving quadratic equations regularly, one common mistake is forgetting to set the equation to zero before applying the quadratic formula. Always rearranging your equation first will help prevent any errors.