Solve the quadratic formula to solve \( -8 x^{2}+10 x+3=0 \) • \( x=\square \) Simplify your answers, using square roots as needed. If there is more than 1 solution, separate the answers with a comma. Question Help: \( \square \) Video Submit Question

To solve the quadratic equation \( -8x^{2} + 10x + 3 = 0 \) using the quadratic formula, follow these steps: ### Quadratic Formula: The quadratic formula is given by: \[ x = \frac{ -b \pm \sqrt{b^{2} - 4ac} }{2a} \] where \( a \), \( b \), and \( c \) are coefficients from the quadratic equation \( ax^{2} + bx + c = 0 \). ### Identify the Coefficients: For the equation \( -8x^{2} + 10x + 3 = 0 \): - \( a = -8 \) - \( b = 10 \) - \( c = 3 \) ### Calculate the Discriminant: \[ \Delta = b^{2} - 4ac = (10)^{2} - 4(-8)(3) = 100 + 96 = 196 \] \[ \sqrt{\Delta} = \sqrt{196} = 14 \] ### Apply the Quadratic Formula: \[ x = \frac{ -10 \pm 14 }{2(-8)} = \frac{ -10 \pm 14 }{ -16 } \] ### Find Both Solutions: 1. **Using the plus sign (+):** \[ x = \frac{ -10 + 14 }{ -16 } = \frac{4}{-16} = -\frac{1}{4} \] 2. **Using the minus sign (−):** \[ x = \frac{ -10 - 14 }{ -16 } = \frac{ -24 }{ -16 } = \frac{24}{16} = \frac{3}{2} \] ### Final Solutions: \[ x = \frac{3}{2},\ -\frac{1}{4} \] **Answer:** \( x = \frac{3}{2},\ -\frac{1}{4} \)