Find the Discriminant -7x^2-5x-3=0

$- 7 x^{2} - 5 x - 3 = 0$

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 $c$ .

${(- 5)}^{2} - 4 (- 7 \cdot - 3)$

Step 3

Evaluate the result to find the discriminant.

Simplify each term.

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

$25 - 4 (- 7 \cdot - 3)$

Multiply $- 4 (- 7 \cdot - 3)$ .

Multiply $- 7$ by $- 3$ .

$25 - 4 \cdot 21$

Multiply $- 4$ by $21$ .

$25 - 84$

Subtract $84$ from $25$ .

$- 59$