Find the Discriminant -9r^2-8r-1=r-r^2-9

$- 9 r^{2} - 8 r - 1 = r - r^{2} - 9$

Move all terms to the left side of the equation and simplify.

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

Subtract $r$ from both sides of the equation.

$- 9 r^{2} - 8 r - 1 - r = - r^{2} - 9$

Add $r^{2}$ to both sides of the equation.

$- 9 r^{2} - 8 r - 1 - r + r^{2} = - 9$

Add $9$ to both sides of the equation.

$- 9 r^{2} - 8 r - 1 - r + r^{2} + 9 = 0$

Simplify $- 9 r^{2} - 8 r - 1 - r + r^{2} + 9$ .

Add $- 9 r^{2}$ and $r^{2}$ .

$- 8 r^{2} - 8 r - 1 - r + 9 = 0$

Subtract $r$ from $- 8 r$ .

$- 8 r^{2} - 9 r - 1 + 9 = 0$

Add $- 1$ and $9$ .

$- 8 r^{2} - 9 r + 8 = 0$

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

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

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

${(- 9)}^{2} - 4 (- 8 \cdot 8)$

Evaluate the result to find the discriminant.

Simplify each term.

Raise $- 9$ to the power of $2$ .

$81 - 4 (- 8 \cdot 8)$

Multiply $- 8$ by $8$ .

$81 - 4 \cdot - 64$

Multiply $- 4$ by $- 64$ .

$81 + 256$

Add $81$ and $256$ .

$337$