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

Did you know that this quadratic equation can be solved using the quadratic formula? The formula \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \) can make finding the roots a breeze! For our equation \( 3x^2 - 2x - 1 = 0 \), the coefficients are \( a = 3 \), \( b = -2 \), and \( c = -1 \). Plug them into the formula, and you’re on your way to discovering the solutions! When solving quadratic equations, a common mistake is neglecting to calculate the discriminant \( b^2 - 4ac \) correctly. If the discriminant is positive, expect two real solutions; if zero, one real solution; and if negative, no real solutions. Always double-check your calculations to avoid these pitfalls and ensure you find the right roots!