Solve by the quadratic formula: \[ -5 x^{2}+13 x+6=0 \] List your answers separated by commas, for example: \( \frac{2}{3}, \frac{5}{2} \) type " \( 2 / 3,5 / 2^{\prime \prime} \) or \( \frac{5 \pm 2 \sqrt{3}}{5} \), type " \( (5+-2 \operatorname{sqrt}(3)) / 5^{\prime \prime} \).

To solve the quadratic equation \(-5x^2 + 13x + 6 = 0\) using the quadratic formula \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\), we first identify the coefficients: \(a = -5\), \(b = 13\), and \(c = 6\). Now, we calculate the discriminant: \[ b^2 - 4ac = 13^2 - 4 \cdot (-5) \cdot 6 = 169 + 120 = 289. \] This is a perfect square! Now we can plug in the values into the formula: \[ x = \frac{-13 \pm \sqrt{289}}{2 \cdot (-5)} = \frac{-13 \pm 17}{-10}. \] Calculating for both cases: 1. \(x = \frac{-13 + 17}{-10} = \frac{4}{-10} = -\frac{2}{5}\), 2. \(x = \frac{-13 - 17}{-10} = \frac{-30}{-10} = 3\). Thus, the solutions are: \(-\frac{2}{5}, 3\)