# How to use the discriminant to find out how many real number roots an equation has for 4x^2 -4x -1 = 0?

$D = {d}^{2} = 16 + 16 = 32 \to d = \pm 4 \sqrt{2}$
$x = \frac{4}{8} \pm \frac{4 \sqrt{2}}{8} = \frac{1}{2} \pm \frac{\sqrt{2}}{2}$