Solve the equation by the quadratic formula. \( 15 x^{2}-11 x-12=0 \) The solution set is \( \{\square \). (Simplify your answer. Type an exact answer, using radicals and \( i \) as need

To solve the quadratic equation \( 15x^2 - 11x - 12 = 0 \) using the quadratic formula, we start by identifying the coefficients: \( a = 15 \), \( b = -11 \), and \( c = -12 \). The quadratic formula is given by: \[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \] Now plug in the values: 1. Calculate the discriminant \( b^2 - 4ac \): \[ (-11)^2 - 4(15)(-12) = 121 + 720 = 841 \] 2. Now apply the quadratic formula: \[ x = \frac{-(-11) \pm \sqrt{841}}{2(15)} = \frac{11 \pm 29}{30} \] 3. Solve for the two values of \( x \): \[ x_1 = \frac{11 + 29}{30} = \frac{40}{30} = \frac{4}{3} \] \[ x_2 = \frac{11 - 29}{30} = \frac{-18}{30} = -\frac{3}{5} \] So the solution set is \( \left\{ \frac{4}{3}, -\frac{3}{5} \right\} \).