Find the Discriminant -4r^2-4r=6

$- 4 r^{2} - 4 r = 6$

Step 1

Subtract $6$ from both sides of the equation.

$- 4 r^{2} - 4 r - 6 = 0$

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 $c$ .

${(- 4)}^{2} - 4 (- 4 \cdot - 6)$

Step 4

Evaluate the result to find the discriminant.

Simplify each term.

Raise $- 4$ to the power of $2$ .

$16 - 4 (- 4 \cdot - 6)$

Multiply $- 4 (- 4 \cdot - 6)$ .

Multiply $- 4$ by $- 6$ .

$16 - 4 \cdot 24$

Multiply $- 4$ by $24$ .

$16 - 96$

Subtract $96$ from $16$ .

$- 80$