Algebra Examples

$2 m^{2} + 3 = m$

Step 1

Subtract $m$ from both sides of the equation.

$2 m^{2} + 3 - m = 0$

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 $c$ .

${(- 1)}^{2} - 4 (2 \cdot 3)$

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 $- 1$ to the power of $2$ .

$1 - 4 (2 \cdot 3)$

Step 4.1.2

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

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Step 4.1.2.1

Multiply $2$ by $3$ .

$1 - 4 \cdot 6$

Step 4.1.2.2

Multiply $- 4$ by $6$ .

$1 - 24$

Step 4.2

Subtract $24$ from $1$ .

$- 23$