a) \( 5 x^{2}-16 x=0 \)

To solve the equation \( 5x^{2} - 16x = 0 \), you can start by factoring out the common term, which in this case is \( x \). This gives you \( x(5x - 16) = 0 \). Setting each factor equal to zero leads to the solutions \( x = 0 \) and \( 5x - 16 = 0 \), which simplifies to \( x = \frac{16}{5} \) or \( 3.2 \). Thus, the solutions are \( x = 0 \) and \( x = 3.2 \). Now, let’s discuss how this quadratic equation reflects practical situations! Quadratic equations often model real-world scenarios like projectile motion or maximizing areas. In business, for instance, similar equations could represent profit margins depending on production levels. Understanding the roots can help in determining break-even points or optimal conditions to enhance performance, making math not just a classroom exercise but a powerful tool in everyday decision-making!