\( 1 \leftarrow \) Solve the equation using any method. \[ 4 x^{2}+7=29 x \] Save The sotation set is \( \} \). P. \( \} .93 \). Points: 0 of 2 (Simplify your answer. Type an exact answer, using radicals and \( i \) as needed. Use a comma to separate answers as needed.)

To solve the equation \( 4x^{2}+7=29x \), we start by rearranging it into a standard quadratic form: \[ 4x^2 - 29x + 7 = 0. \] Next, we can apply the quadratic formula \( x = \frac{-b \pm \sqrt{b^2-4ac}}{2a} \), where \( a = 4 \), \( b = -29 \), and \( c = 7 \). Calculating the discriminant: \[ b^2 - 4ac = (-29)^2 - 4 \cdot 4 \cdot 7 = 841 - 112 = 729. \] Now substituting back into the quadratic formula: \[ x = \frac{29 \pm \sqrt{729}}{2 \cdot 4} = \frac{29 \pm 27}{8}. \] This gives us two solutions: 1. \( x = \frac{56}{8} = 7 \) 2. \( x = \frac{2}{8} = \frac{1}{4} \) Therefore, the solution set is \( \{ 7, \frac{1}{4} \} \).