Solve the quadratic equation. \[ 4 x^{2}+8 x-3=0 \] Write one exact solution in each box. You can add or remove boxes. If there are no real solutions, remove all boxes.

To solve the quadratic equation \( 4x^{2} + 8x - 3 = 0 \), we can use the quadratic formula, which is given by: \[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \] Here, \( a = 4 \), \( b = 8 \), and \( c = -3 \). Let's calculate the discriminant: \[ b^2 - 4ac = 8^2 - 4 \cdot 4 \cdot (-3) = 64 + 48 = 112 \] Now substituting back into the quadratic formula: \[ x = \frac{-8 \pm \sqrt{112}}{2 \cdot 4} \] We can simplify \( \sqrt{112} \) to \( \sqrt{16 \cdot 7} = 4\sqrt{7} \). Therefore, our equation now looks like this: \[ x = \frac{-8 \pm 4\sqrt{7}}{8} \] Simplifying gives: \[ x = \frac{-2 \pm \sqrt{7}}{2} \] The two exact solutions are: \[ \frac{-2 + \sqrt{7}}{2} \] \[ \frac{-2 - \sqrt{7}}{2} \]