Use the quadratic formula to solve for \( x \). \[ 5 x^{2}+3 x=3 \] Round your answer to the nearest hundredth. If there is more than one solution, separate them with commas.

To solve the equation \( 5x^2 + 3x - 3 = 0 \) using the quadratic formula, we identify \( a = 5 \), \( b = 3 \), and \( c = -3 \). The quadratic formula is given by: \[ x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}} \] Calculating the discriminant: \[ b^2 - 4ac = 3^2 - 4(5)(-3) = 9 + 60 = 69 \] Now substituting the values into the formula: \[ x = \frac{{-3 \pm \sqrt{69}}}{{2 \cdot 5}} = \frac{{-3 \pm \sqrt{69}}}{10} \] Calculating \( \sqrt{69} \) gives approximately \( 8.31 \): \[ x = \frac{{-3 + 8.31}}{10} \quad \text{and} \quad x = \frac{{-3 - 8.31}}{10} \] Thus, the solutions are: \[ x \approx \frac{5.31}{10} \approx 0.53 \quad \text{and} \quad x \approx \frac{-11.31}{10} \approx -1.13 \] So, rounding to the nearest hundredth, the solutions are: **Final Answers:** \( x \approx 0.53, -1.13 \)