Solve for m m^2-2/3m=1/3

$m^{2} - \frac{2}{3} m = \frac{1}{3}$

Simplify each term.

Combine $m$ and $\frac{2}{3}$ .

$m^{2} - \frac{m \cdot 2}{3} = \frac{1}{3}$

Move $2$ to the left of $m$ .

$m^{2} - \frac{2 m}{3} = \frac{1}{3}$

Subtract $\frac{1}{3}$ from both sides of the equation.

$m^{2} - \frac{2 m}{3} - \frac{1}{3} = 0$

Multiply through by the least common denominator $3$ , then simplify.

Apply the distributive property.

$3 m^{2} + 3 (- \frac{2 m}{3}) + 3 (- \frac{1}{3}) = 0$

Simplify.

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{2 m}{3}$ into the numerator.

$3 m^{2} + 3 (\frac{- 2 m}{3}) + 3 (- \frac{1}{3}) = 0$

Cancel the common factor.

$3 m^{2} + 3 (\frac{- 2 m}{3}) + 3 (- \frac{1}{3}) = 0$

Rewrite the expression.

$3 m^{2} - 2 m + 3 (- \frac{1}{3}) = 0$

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{1}{3}$ into the numerator.

$3 m^{2} - 2 m + 3 (\frac{- 1}{3}) = 0$

Cancel the common factor.

$3 m^{2} - 2 m + 3 (\frac{- 1}{3}) = 0$

Rewrite the expression.

$3 m^{2} - 2 m - 1 = 0$

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Substitute the values $a = 3$ , $b = - 2$ , and $c = - 1$ into the quadratic formula and solve for $m$ .

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

Simplify.

Simplify the numerator.

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

$m = \frac{2 \pm \sqrt{4 - 4 \cdot 3 \cdot - 1}}{2 \cdot 3}$

Multiply $- 4$ by $3$ .

$m = \frac{2 \pm \sqrt{4 - 12 \cdot - 1}}{2 \cdot 3}$

Multiply $- 12$ by $- 1$ .

$m = \frac{2 \pm \sqrt{4 + 12}}{2 \cdot 3}$

Add $4$ and $12$ .

$m = \frac{2 \pm \sqrt{16}}{2 \cdot 3}$

Rewrite $16$ as $4^{2}$ .

$m = \frac{2 \pm \sqrt{4^{2}}}{2 \cdot 3}$

Pull terms out from under the radical, assuming positive real numbers.

$m = \frac{2 \pm 4}{2 \cdot 3}$

Multiply $2$ by $3$ .

$m = \frac{2 \pm 4}{6}$

Simplify $\frac{2 \pm 4}{6}$ .

$m = \frac{1 \pm 2}{3}$

The final answer is the combination of both solutions.

$m = 1, - \frac{1}{3}$

The result can be shown in multiple forms.

Exact Form:

$m = 1, - \frac{1}{3}$

Decimal Form:

$m = 1, - 0.\overline{3}$

Solve for m m^2-2/3m=1/3

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