Evaluate the discriminant and determine the number and type of solutions to the eq \[ 4 x^{2}-5 x+3=0 \] Part: \( 0 / 2 \) Part 1 of 2

To evaluate the discriminant of the equation \( 4x^{2}-5x+3=0 \), we use the formula for the discriminant, \( D = b^2 - 4ac \), where \( a = 4 \), \( b = -5 \), and \( c = 3 \). Calculating it: \[ D = (-5)^2 - 4 \times 4 \times 3 = 25 - 48 = -23 \] Since the discriminant \( D = -23 \) is less than zero, this means that the quadratic equation has two complex solutions (no real solutions). You can think of these solutions as "imaginary friends" that exist in a different realm!