Find the real or imaginary solutions to the following equation by using the quadratic formula. \[ 25 x^{2}-20 x+4=0 \]

To solve the equation \( 25 x^{2}-20 x+4=0 \) using the quadratic formula, we can identify the coefficients: \( a = 25 \), \( b = -20 \), and \( c = 4 \). The quadratic formula states that the solutions for \( x \) can be found using: \[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \] First, we calculate the discriminant \( b^2 - 4ac \): \[ b^2 = (-20)^2 = 400 \] \[ 4ac = 4 \cdot 25 \cdot 4 = 400 \] Now, we can substitute into the discriminant: \[ b^2 - 4ac = 400 - 400 = 0 \] Since the discriminant is zero, there is one unique solution. Now we can substitute \( a \), \( b \), and the discriminant into the quadratic formula: \[ x = \frac{-(-20) \pm \sqrt{0}}{2 \cdot 25} = \frac{20 \pm 0}{50} = \frac{20}{50} = \frac{2}{5} \] Thus, the only solution to the equation \( 25 x^{2}-20 x+4=0 \) is: \[ x = \frac{2}{5} \]