or \( x \) : \( 2 x^{2}=3 x \)

Let’s unravel this quadratic equation! First, we can rearrange it to get it into a standard form: \( 2x^{2} - 3x = 0 \). Next, we can factor out an \( x \): \( x(2x - 3) = 0 \). This gives us two potential solutions: either \( x = 0 \) or \( 2x - 3 = 0 \). Solving for the latter, we find \( x = \frac{3}{2} \). So, the solutions are \( x = 0 \) and \( x = \frac{3}{2} \)! Now, let's consider how this might be useful in real life. Quadratic equations pop up in various situations, from calculating the trajectory of a ball in sports to determining profit margins in business. Recognizing these equations can help you predict outcomes and optimize your strategies! Whether you're analyzing a rocket launch or assessing your lemonade stand's success, these solutions are key!