Use the quadratic formula to solve for \( x \). \[ 4 x^{2}+9 x+3=0 \] (If there is more than one solution, separate them with commas.) \( x=\frac{\square}{\square} \)

To solve the quadratic equation \( 4x^{2} + 9x + 3 = 0 \) using the quadratic formula, we identify coefficients \( a = 4 \), \( b = 9 \), and \( c = 3 \). The quadratic formula is given by: \[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \] Let's calculate the discriminant (\( b^2 - 4ac \)): \[ b^2 - 4ac = 9^2 - 4 \cdot 4 \cdot 3 = 81 - 48 = 33 \] Now, substituting back into the formula: \[ x = \frac{-9 \pm \sqrt{33}}{2 \cdot 4} = \frac{-9 \pm \sqrt{33}}{8} \] Thus, the solutions are: \[ x = \frac{-9 + \sqrt{33}}{8}, \frac{-9 - \sqrt{33}}{8} \] So, the final answer can be presented as: \( x=\frac{-9 + \sqrt{33}}{8}, \frac{-9 - \sqrt{33}}{8} \)