Find the Discriminant x^2+5x+9=-3x-3

$x^{2} + 5 x + 9 = - 3 x - 3$

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

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

Add $3 x$ to both sides of the equation.

$x^{2} + 5 x + 9 + 3 x = - 3$

Add $3$ to both sides of the equation.

$x^{2} + 5 x + 9 + 3 x + 3 = 0$

Simplify $x^{2} + 5 x + 9 + 3 x + 3$ .

Add $5 x$ and $3 x$ .

$x^{2} + 8 x + 9 + 3 = 0$

Add $9$ and $3$ .

$x^{2} + 8 x + 12 = 0$

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 $c$ .

$8^{2} - 4 (1 \cdot 12)$

Evaluate the result to find the discriminant.

Simplify each term.

Raise $8$ to the power of $2$ .

$64 - 4 (1 \cdot 12)$

Multiply $12$ by $1$ .

$64 - 4 \cdot 12$

Multiply $- 4$ by $12$ .

$64 - 48$

Subtract $48$ from $64$ .

$16$