# How do you find the discriminant and how many solutions does 4d^2 - 8d + 3= 0 have?

Discriminant $D = {d}^{2} = {b}^{2} - 4 a c = 64 - 48 = 16$ --> d = 4 and d = -4. There are 2 solutions, called real roots.
$x 1 = - \frac{b}{2} a + \frac{d}{2} a = \frac{8}{8} + \frac{4}{8} = \frac{12}{8} = \frac{3}{2}$
$x 2 = - \frac{b}{2} a - \frac{d}{2} a = \frac{8}{8} - \frac{4}{8} = \frac{4}{8} = \frac{1}{2.}$