# What is the discriminant of 8x^2+5x+6=0 and what does that mean?

Jul 18, 2015

The discriminant $\Delta$ can be:
$\Delta > 0$ $\implies$ your equation has 2 distinct Real solutions;
$\Delta = 0$ $\implies$ your equation has 2 coincident Real solutions;
$\Delta < 0$ $\implies$ your equation does not have Real solutions.

#### Explanation:

The discriminant $\Delta$ is a number that characterizes the solutions of a second degree equatin and is given as:
$\Delta = {b}^{2} - 4 a c$
Your equation is in the form $a {x}^{2} + b x + c = 0$ with:
$a = 8$
$b = 5$
$c = 6$
So $\Delta = 25 - 4 \left(8 \cdot 6\right) = 25 - 192 = - 167 < 0$
A negative discriminant means that your equation does not have Real solutions!