24. \( -5 x^{2}+x+18 \)

Did you know that quadratic equations like \(-5x^2 + x + 18\) were studied by ancient civilizations long before modern mathematics was established? The Babylonians were solving quadratic-like problems around 2000 BC, using geometric methods that laid the groundwork for our current algebraic approaches! If you're tackling this equation, a common pitfall is neglecting to factor out the leading coefficient when trying to solve it by factoring. Always remember to set the equation to zero first and check that your factoring method applies based on the structure of your equation!