ssignment Question 35, 3.3.69 HW Score: 48.75\%, 23.89 Solve the equation. \[ 3 x^{2}+5=7 x \] \[ x= \] \( \square \) (Use a comma to separate answers as needed. Type an exact answer, using radicals and \( i \) as needed.)

To solve the equation \(3 x^{2} + 5 = 7 x\), we first rearrange it into standard form: \[ 3 x^{2} - 7 x + 5 = 0. \] Next, we can use the quadratic formula \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\), where \(a = 3\), \(b = -7\), and \(c = 5\). Plugging in these values, we compute: 1. The discriminant: \[ b^2 - 4ac = (-7)^2 - 4(3)(5) = 49 - 60 = -11. \] 2. Since the discriminant is negative, we have complex solutions. Now applying the quadratic formula: \[ x = \frac{7 \pm \sqrt{-11}}{2(3)} = \frac{7 \pm i\sqrt{11}}{6}. \] Thus, the solutions are: \[ x = \frac{7 + i\sqrt{11}}{6}, \frac{7 - i\sqrt{11}}{6}. \] So, \( x = \frac{7 + i\sqrt{11}}{6}, \frac{7 - i\sqrt{11}}{6} \).