Solve for m 3m^2+5m=6

$3 m^{2} + 5 m = 6$

Step 1

Subtract $6$ from both sides of the equation.

$3 m^{2} + 5 m - 6 = 0$

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 $a = 3$ , $b = 5$ , and $c = - 6$ into the quadratic formula and solve for $m$ .

$\frac{- 5 \pm \sqrt{5^{2} - 4 \cdot (3 \cdot - 6)}}{2 \cdot 3}$

Step 4

Simplify.

Simplify the numerator.

Raise $5$ to the power of $2$ .

$m = \frac{- 5 \pm \sqrt{25 - 4 \cdot 3 \cdot - 6}}{2 \cdot 3}$

Multiply $- 4 \cdot 3 \cdot - 6$ .

Multiply $- 4$ by $3$ .

$m = \frac{- 5 \pm \sqrt{25 - 12 \cdot - 6}}{2 \cdot 3}$

Multiply $- 12$ by $- 6$ .

$m = \frac{- 5 \pm \sqrt{25 + 72}}{2 \cdot 3}$

Add $25$ and $72$ .

$m = \frac{- 5 \pm \sqrt{97}}{2 \cdot 3}$

Multiply $2$ by $3$ .

$m = \frac{- 5 \pm \sqrt{97}}{6}$

Step 5

The final answer is the combination of both solutions.

$m = - \frac{5 - \sqrt{97}}{6}, - \frac{5 + \sqrt{97}}{6}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$m = - \frac{5 - \sqrt{97}}{6}, - \frac{5 + \sqrt{97}}{6}$

Decimal Form:

$m = 0.80814296 \dots, - 2.47480963 \dots$