5x²+8x-4=0

To solve the quadratic equation \( 5x^2 + 8x - 4 = 0 \), you can use the quadratic formula: \[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \] where \( a = 5 \), \( b = 8 \), and \( c = -4 \). First, calculate the discriminant \( b^2 - 4ac \): \[ b^2 = 8^2 = 64 \] \[ 4ac = 4 \cdot 5 \cdot (-4) = -80 \] \[ b^2 - 4ac = 64 - (-80) = 64 + 80 = 144 \] Now plug the values into the quadratic formula: \[ x = \frac{-8 \pm \sqrt{144}}{2 \cdot 5} \] \[ x = \frac{-8 \pm 12}{10} \] Now, calculate the two possible values for \( x \): 1. \( x = \frac{-8 + 12}{10} = \frac{4}{10} = \frac{2}{5} \) 2. \( x = \frac{-8 - 12}{10} = \frac{-20}{10} = -2 \) Thus, the solutions to the equation \( 5x^2 + 8x - 4 = 0 \) are: \[ x = \frac{2}{5} \quad \text{and} \quad x = -2 \]