Find the Discriminant -18p=p^2+81

$- 18 p = p^{2} + 81$

Step 1

Move all the expressions to the left side of the equation.

Subtract $p^{2}$ from both sides of the equation.

$- 18 p - p^{2} = 81$

Subtract $81$ from both sides of the equation.

$- 18 p - p^{2} - 81 = 0$

Step 2

The discriminant of a quadratic is the expression inside the radical of the quadratic formula.

$b^{2} - 4 (a c)$

Step 3

Substitute in the values of $a$ , $b$ , and $c$ .

${(- 18)}^{2} - 4 (- - 81)$

Step 4

Evaluate the result to find the discriminant.

Simplify each term.

Raise $- 18$ to the power of $2$ .

$324 - 4 (- - 81)$

Multiply $- 4 (- - 81)$ .

Multiply $- 1$ by $- 81$ .

$324 - 4 \cdot 81$

Multiply $- 4$ by $81$ .

$324 - 324$

Subtract $324$ from $324$ .

$0$