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

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

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 $c$ .

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

Step 3

Evaluate the result to find the discriminant.

Simplify each term.

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

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

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

Multiply $7$ by $- 3$ .

$4 - 4 \cdot - 21$

Multiply $- 4$ by $- 21$ .

$4 + 84$

Add $4$ and $84$ .

$88$