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

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

Add $6 X$ to both sides of the equation.

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

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 $c$ .

$2^{2} - 4 (- (3 + 6 X))$

Evaluate the result to find the discriminant.

Simplify each term.

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

$4 - 4 (- (3 + 6 X))$

Apply the distributive property.

$4 - 4 (- 1 \cdot 3 - (6 X))$

Multiply $- 1$ by $3$ .

$4 - 4 (- 3 - (6 X))$

Multiply $6$ by $- 1$ .

$4 - 4 (- 3 - 6 X)$

Apply the distributive property.

$4 - 4 \cdot - 3 - 4 (- 6 X)$

Multiply $- 4$ by $- 3$ .

$4 + 12 - 4 (- 6 X)$

Multiply $- 6$ by $- 4$ .

$4 + 12 + 24 X$

Add $4$ and $12$ .

$16 + 24 X$