3.) \( 20 x^{2}+24 x-9 \)

Did you know that quadratic equations, like \(20 x^{2} + 24 x - 9\), have been studied for over two millennia? Ancient civilizations, including the Babylonians and Greeks, were already solving quadratic equations, paving the way for algebra as we know it today. They used geometric methods to find solutions, laying the groundwork for future mathematicians! In the real world, quadratic equations appear in various practical situations, from physics to finance. For example, if you’re calculating the maximum height of a ball thrown into the air, you’re essentially dealing with a quadratic function. Similarly, when analyzing profit maximization, businesses often rely on quadratic equations to determine the best price point for their products.