Solve the quadratic formula to solve \( 9 x^{2}=24 x-11 \). \[ x=\square \] Simplify your answers, using square roots as needed. If there is more than 1 solution, separate the answers with a comma. For example: \( \frac{2}{3}, \frac{5}{2} \) type " \( 2 / 3,5 / 2 \) " or \( \frac{5+2 \sqrt{3}}{5} \), type " (5+2sqrt(3))/5". Question Help: \( \square \) Video Submit Question

To solve the quadratic equation \( 9x^2 = 24x - 11 \), first, rearrange it into standard form: \[ 9x^2 - 24x + 11 = 0. \] Now, apply the quadratic formula, \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \), where \( a = 9 \), \( b = -24 \), and \( c = 11 \). Calculating the discriminant: \[ b^2 - 4ac = (-24)^2 - 4 \cdot 9 \cdot 11 = 576 - 396 = 180. \] Now, plug the values into the formula: \[ x = \frac{-(-24) \pm \sqrt{180}}{2 \cdot 9} = \frac{24 \pm \sqrt{180}}{18}. \] Next, simplify \( \sqrt{180} \): \[ \sqrt{180} = \sqrt{36 \cdot 5} = 6\sqrt{5}. \] So, the expression for \( x \) becomes: \[ x = \frac{24 \pm 6\sqrt{5}}{18}. \] Now, simplify this fraction: \[ x = \frac{12 \pm 3\sqrt{5}}{9} = \frac{4 \pm \sqrt{5}}{3}. \] Thus, the final simplified answers are: \[ x = \frac{4 + \sqrt{5}}{3}, \frac{4 - \sqrt{5}}{3}. \] Save your answers in the requested format: \( (4+\sqrt(5))/3,(4-\sqrt(5))/3 \)