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

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

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 $c$ .

$0^{2} - 4 (9 (- 3 n + 2))$

Step 3

Evaluate the result to find the discriminant.

Simplify each term.

Raising $0$ to any positive power yields $0$ .

$0 - 4 (9 (- 3 n + 2))$

Apply the distributive property.

$0 - 4 (9 (- 3 n) + 9 \cdot 2)$

Multiply $- 3$ by $9$ .

$0 - 4 (- 27 n + 9 \cdot 2)$

Multiply $9$ by $2$ .

$0 - 4 (- 27 n + 18)$

Apply the distributive property.

$0 - 4 (- 27 n) - 4 \cdot 18$

Multiply $- 27$ by $- 4$ .

$0 + 108 n - 4 \cdot 18$

Multiply $- 4$ by $18$ .

$0 + 108 n - 72$

Add $0$ and $108 n$ .

$108 n - 72$