6) \( 5 k^{2}+13 k+6 \)

Did you know that quadratic equations like \( 5 k^{2}+13 k+6 \) can be solved using the quadratic formula? The formula is \( k = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \), where \( a \), \( b \), and \( c \) are the coefficients from the equation \( ax^2 + bx + c = 0 \). In this case, \( a = 5 \), \( b = 13 \), and \( c = 6 \). Plugging in these values helps you find the roots, or solutions, of the equation! When working with quadratics, a common mistake is forgetting to simplify your final answer. After applying the quadratic formula, always check if your result can be simplified further. For example, double-check your calculation of the discriminant \( b^2 - 4ac \) for any mistakes, since it plays a crucial role in determining if your solutions are real or imaginary (or if they can be simplified)!