Find the Discriminant 3x^2+5x-9=0

$3 x^{2} + 5 x - 9 = 0$

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 $c$ .

$5^{2} - 4 (3 \cdot - 9)$

Step 3

Evaluate the result to find the discriminant.

Simplify each term.

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

$25 - 4 (3 \cdot - 9)$

Multiply $- 4 (3 \cdot - 9)$ .

Multiply $3$ by $- 9$ .

$25 - 4 \cdot - 27$

Multiply $- 4$ by $- 27$ .

$25 + 108$

Add $25$ and $108$ .

$133$