Find the Discriminant 9m^2+6m+6=5

$9 m^{2} + 6 m + 6 = 5$

Step 1

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

Subtract $5$ from both sides of the equation.

$9 m^{2} + 6 m + 6 - 5 = 0$

Subtract $5$ from $6$ .

$9 m^{2} + 6 m + 1 = 0$

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 $c$ .

$6^{2} - 4 (9 \cdot 1)$

Step 4

Evaluate the result to find the discriminant.

Simplify each term.

Raise $6$ to the power of $2$ .

$36 - 4 (9 \cdot 1)$

Multiply $- 4 (9 \cdot 1)$ .

Multiply $9$ by $1$ .

$36 - 4 \cdot 9$

Multiply $- 4$ by $9$ .

$36 - 36$

Subtract $36$ from $36$ .

$0$