3. Determine the value of the \( x \) intercepts of the quadratic: \[ 3 x^{2}+7 x=-2 \]

To find the x-intercepts of the quadratic equation \( 3x^{2} + 7x + 2 = 0 \), we can rearrange the given equation as follows: 1. Start with the equation: \[ 3x^{2} + 7x + 2 = 0 \] 2. Use the quadratic formula \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \), where \( a = 3 \), \( b = 7 \), and \( c = 2 \). 3. Calculate the discriminant: \[ b^2 - 4ac = 7^2 - 4(3)(2) = 49 - 24 = 25 \] 4. Plug the values into the quadratic formula: \[ x = \frac{-7 \pm \sqrt{25}}{2 \cdot 3} = \frac{-7 \pm 5}{6} \] 5. Calculate the two possible values for \( x \): - \( x = \frac{-7 + 5}{6} = \frac{-2}{6} = -\frac{1}{3} \) - \( x = \frac{-7 - 5}{6} = \frac{-12}{6} = -2 \) Thus, the x-intercepts of the quadratic are \( x = -\frac{1}{3} \) and \( x = -2 \).