Find the Discriminant -6x^2+12x+12=-7x^2-2

$- 6 x^{2} + 12 x + 12 = - 7 x^{2} - 2$

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 $7 x^{2}$ to both sides of the equation.

$- 6 x^{2} + 12 x + 12 + 7 x^{2} = - 2$

Add $2$ to both sides of the equation.

$- 6 x^{2} + 12 x + 12 + 7 x^{2} + 2 = 0$

Simplify $- 6 x^{2} + 12 x + 12 + 7 x^{2} + 2$ .

Add $- 6 x^{2}$ and $7 x^{2}$ .

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

Add $12$ and $2$ .

$x^{2} + 12 x + 14 = 0$

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 $c$ .

$12^{2} - 4 (1 \cdot 14)$

Step 4

Evaluate the result to find the discriminant.

Simplify each term.

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

$144 - 4 (1 \cdot 14)$

Multiply $- 4 (1 \cdot 14)$ .

Multiply $14$ by $1$ .

$144 - 4 \cdot 14$

Multiply $- 4$ by $14$ .

$144 - 56$

Subtract $56$ from $144$ .

$88$