a. \( 3 x^{2}-2 x-1=0 \)

Did you know that quadratic equations like \(3x^{2}-2x-1=0\) can be solved using the quadratic formula? It states that for any equation in the form \(ax^2 + bx + c = 0\), the solutions for \(x\) can be found using \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\). For this equation, \(a = 3\), \(b = -2\), and \(c = -1\), so just plug in these values and watch the magic happen! Ever wondered how quadratic equations pop up in real life? From projectile motion to determining the optimal area for a garden, they’re everywhere! When you want to find the height of a thrown ball over time or optimize your profit in a business, understanding how to solve these equations opens a world of possibilities. So, embrace your inner mathematician and explore the practical side of quadratics!