Find the Discriminant x^2+3x=-2x-6

$x^{2} + 3 x = - 2 x - 6$

Step 1

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

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

Add $2 x$ to both sides of the equation.

$x^{2} + 3 x + 2 x = - 6$

Add $6$ to both sides of the equation.

$x^{2} + 3 x + 2 x + 6 = 0$

Add $3 x$ and $2 x$ .

$x^{2} + 5 x + 6 = 0$

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 $c$ .

$5^{2} - 4 (1 \cdot 6)$

Step 4

Evaluate the result to find the discriminant.

Simplify each term.

Raise $5$ to the power of $2$ .

$25 - 4 (1 \cdot 6)$

Multiply $- 4 (1 \cdot 6)$ .

Multiply $6$ by $1$ .

$25 - 4 \cdot 6$

Multiply $- 4$ by $6$ .

$25 - 24$

Subtract $24$ from $25$ .

$1$