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.
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The Deep Dive
To solve the equation \( 5x^2 = 6x \), we first rearrange it into standard form: \( 5x^2 - 6x = 0 \). We can factor this as \( x(5x - 6) = 0 \), giving us two potential solutions: \( x = 0 \) and \( 5x - 6 = 0 \). For the second equation, \( 5x = 6 \) leads to \( x = \frac{6}{5} \). Thus, the solution set is \( \{0, \frac{6}{5}\} \). If you ever find yourself stuck in a similar quadratic equation situation, remember to always bring everything to one side first! A common mistake is forgetting to set the equation to zero, which can lead to missed solutions. Once in standard form, utilize the quadratic formula or factoring to find your answers efficiently. Happy problem-solving!