Solve for m 3m^2+7m=2

$3 m^{2} + 7 m = 2$

Step 1

Subtract $2$ from both sides of the equation.

$3 m^{2} + 7 m - 2 = 0$

Step 2

Use the quadratic formula to find the solutions.

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

Step 3

Substitute the values $a = 3$ , $b = 7$ , and $c = - 2$ into the quadratic formula and solve for $m$ .

$\frac{- 7 \pm \sqrt{7^{2} - 4 \cdot (3 \cdot - 2)}}{2 \cdot 3}$

Step 4

Simplify.

Simplify the numerator.

Raise $7$ to the power of $2$ .

$m = \frac{- 7 \pm \sqrt{49 - 4 \cdot 3 \cdot - 2}}{2 \cdot 3}$

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

Multiply $- 4$ by $3$ .

$m = \frac{- 7 \pm \sqrt{49 - 12 \cdot - 2}}{2 \cdot 3}$

Multiply $- 12$ by $- 2$ .

$m = \frac{- 7 \pm \sqrt{49 + 24}}{2 \cdot 3}$

Add $49$ and $24$ .

$m = \frac{- 7 \pm \sqrt{73}}{2 \cdot 3}$

Multiply $2$ by $3$ .

$m = \frac{- 7 \pm \sqrt{73}}{6}$

Step 5

The final answer is the combination of both solutions.

$m = - \frac{7 - \sqrt{73}}{6}, - \frac{7 + \sqrt{73}}{6}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$m = - \frac{7 - \sqrt{73}}{6}, - \frac{7 + \sqrt{73}}{6}$

Decimal Form:

$m = 0.25733395 \dots, - 2.59066729 \dots$