Algebra Examples

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

Step 1

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

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

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 $c$ .

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

Step 4

Evaluate the result to find the discriminant.

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Step 4.1

Simplify each term.

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Step 4.1.1

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

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

Step 4.1.2

Apply the distributive property.

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

Step 4.1.3

Multiply $- 1$ by $3$ .

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

Step 4.1.4

Multiply $6$ by $- 1$ .

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

Step 4.1.5

Apply the distributive property.

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

Step 4.1.6

Multiply $- 4$ by $- 3$ .

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

Step 4.1.7

Multiply $- 6$ by $- 4$ .

$4 + 12 + 24 X$

Step 4.2

Add $4$ and $12$ .

$16 + 24 X$