Find the Discriminant -3x^2-5x-6=0

$- 3 x^{2} - 5 x - 6 = 0$

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 $c$ .

${(- 5)}^{2} - 4 (- 3 \cdot - 6)$

Step 3

Evaluate the result to find the discriminant.

Simplify each term.

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

$25 - 4 (- 3 \cdot - 6)$

Multiply $- 4 (- 3 \cdot - 6)$ .

Multiply $- 3$ by $- 6$ .

$25 - 4 \cdot 18$

Multiply $- 4$ by $18$ .

$25 - 72$

Subtract $72$ from $25$ .

$- 47$