Find the Discriminant x^2+8x+54=-4x

$x^{2} + 8 x + 54 = - 4 x$

Step 1

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

Add $4 x$ to both sides of the equation.

$x^{2} + 8 x + 54 + 4 x = 0$

Add $8 x$ and $4 x$ .

$x^{2} + 12 x + 54 = 0$

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 $c$ .

$12^{2} - 4 (1 \cdot 54)$

Step 4

Evaluate the result to find the discriminant.

Simplify each term.

Raise $12$ to the power of $2$ .

$144 - 4 (1 \cdot 54)$

Multiply $- 4 (1 \cdot 54)$ .

Multiply $54$ by $1$ .

$144 - 4 \cdot 54$

Multiply $- 4$ by $54$ .

$144 - 216$

Subtract $216$ from $144$ .

$- 72$