Algebra Examples

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

Step 1

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

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Step 1.1

Subtract $2 x^{2}$ from both sides of the equation.

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

Step 1.2

Subtract $6 x$ from both sides of the equation.

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

Step 1.3

Subtract $3$ from both sides of the equation.

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

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 $c$ .

${(- 6)}^{2} - 4 (- 2 \cdot - 3)$

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 $- 6$ to the power of $2$ .

$36 - 4 (- 2 \cdot - 3)$

Step 4.1.2

Multiply $- 4 (- 2 \cdot - 3)$ .

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Step 4.1.2.1

Multiply $- 2$ by $- 3$ .

$36 - 4 \cdot 6$

Step 4.1.2.2

Multiply $- 4$ by $6$ .

$36 - 24$

Step 4.2

Subtract $24$ from $36$ .

$12$