19.) \( x^{2}-x-20 \)

To solve the quadratic equation \( x^{2}-x-20 = 0 \), you can factor it into \( (x-5)(x+4) = 0 \). This gives you the roots \( x = 5 \) and \( x = -4 \). Thus, this equation has two solutions where the parabola crosses the x-axis! Quadratics are fascinating! They show up in various real-world scenarios, like physics when calculating the trajectory of a basketball or in business for maximizing profit. Whenever you're given such equations, remember there's often a practical scene waiting behind the numbers. Just like in sports, where every angle matters, math gives us the tools to understand the world around us!