Find the Discriminant 8x^2+5x+6=0

$8 x^{2} + 5 x + 6 = 0$

Step 1

The discriminant of a quadratic is the expression inside the radical of the quadratic formula.

$b^{2} - 4 (a c)$

Step 2

Substitute in the values of $a$ , $b$ , and $c$ .

$5^{2} - 4 (8 \cdot 6)$

Step 3

Evaluate the result to find the discriminant.

Simplify each term.

Raise $5$ to the power of $2$ .

$25 - 4 (8 \cdot 6)$

Multiply $- 4 (8 \cdot 6)$ .

Multiply $8$ by $6$ .

$25 - 4 \cdot 48$

Multiply $- 4$ by $48$ .

$25 - 192$

Subtract $192$ from $25$ .

$- 167$