Solve the quadratic formula to solve \( 4 x^{2}=16 x-13 \). \[ x=\square \] Simplify your answers, using square roots as needed. If there is more than 1 solution, separate the answers with a comma. Question Help: \( \square \) Video Submit Question

To solve the quadratic equation \( 4x^{2} - 16x + 13 = 0 \), we can use the quadratic formula \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \). Here, \( a = 4 \), \( b = -16 \), and \( c = 13 \). First, calculate the discriminant: \[ b^2 - 4ac = (-16)^{2} - 4(4)(13) = 256 - 208 = 48. \] Now plug the values into the quadratic formula: \[ x = \frac{-(-16) \pm \sqrt{48}}{2(4)} = \frac{16 \pm 4\sqrt{3}}{8}. \] This simplifies to: \[ x = 2 \pm \frac{\sqrt{3}}{2}. \] Thus, the solutions are: \[ x = 2 + \frac{\sqrt{3}}{2}, \quad x = 2 - \frac{\sqrt{3}}{2}. \]