a) \( x^{2}-5 x-14=0 \)

Did you know that quadratic equations like this one have been around since ancient civilizations? The Babylonians were solving quadratic equations as far back as 2000 BC, using geometric methods that laid the groundwork for algebra! Their approach was quite different from ours today, as they relied on visualizing the problems rather than the symbolic notation we’re accustomed to. When solving a quadratic equation, always remember to check for possible mistakes. One common pitfall is mixing up the signs when applying the quadratic formula \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \). For this equation, make sure you correctly calculate the discriminant (\(b^2 - 4ac\)) to ensure you're not missing any real or complex solutions!