8) \( 2 n^{2}+n-21 \)

Did you know that quadratic equations, like \( 2n^{2} + n - 21 \), have a rich history dating back to ancient Babylon, where mathematicians already grappling with similar problems? They used geometric methods to solve them long before the formal development of algebra! Fast forward to today, and we have the quadratic formula, which makes solving these equations much more straightforward. For real-world applications, quadratic equations show up everywhere, from projectile motion to economics! Whether you’re calculating the trajectory of a basketball shot or maximizing profit in a business model, these equations provide crucial insights. Each solution represents points of interest, such as crucial turning points in a graph that can signify maximum or minimum values.