Solve for m 4m^2+7m=6

$4 m^{2} + 7 m = 6$

Step 1

Subtract $6$ from both sides of the equation.

$4 m^{2} + 7 m - 6 = 0$

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 $a = 4$ , $b = 7$ , and $c = - 6$ into the quadratic formula and solve for $m$ .

$\frac{- 7 \pm \sqrt{7^{2} - 4 \cdot (4 \cdot - 6)}}{2 \cdot 4}$

Step 4

Simplify.

Simplify the numerator.

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

$m = \frac{- 7 \pm \sqrt{49 - 4 \cdot 4 \cdot - 6}}{2 \cdot 4}$

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

Multiply $- 4$ by $4$ .

$m = \frac{- 7 \pm \sqrt{49 - 16 \cdot - 6}}{2 \cdot 4}$

Multiply $- 16$ by $- 6$ .

$m = \frac{- 7 \pm \sqrt{49 + 96}}{2 \cdot 4}$

Add $49$ and $96$ .

$m = \frac{- 7 \pm \sqrt{145}}{2 \cdot 4}$

Multiply $2$ by $4$ .

$m = \frac{- 7 \pm \sqrt{145}}{8}$

Step 5

The final answer is the combination of both solutions.

$m = - \frac{7 - \sqrt{145}}{8}, - \frac{7 + \sqrt{145}}{8}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$m = - \frac{7 - \sqrt{145}}{8}, - \frac{7 + \sqrt{145}}{8}$

Decimal Form:

$m = 0.63019932 \dots, - 2.38019932 \dots$