Solve for m 4m^2-3m=n

$4 m^{2} - 3 m = n$

Move $n$ to the left side of the equation by subtracting it from both sides.

$4 m^{2} - 3 m - n = 0$

Use the quadratic formula to find the solutions.

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

Substitute the values $a = 4$ , $b = - 3$ , and $c = - n$ into the quadratic formula and solve for $m$ .

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

Simplify.

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Simplify the numerator.

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Raise $- 3$ to the power of $2$ .

$m = \frac{3 \pm \sqrt{9 - 4 \cdot (4 \cdot (- n))}}{2 \cdot 4}$

Multiply $- 1$ by $4$ .

$m = \frac{3 \pm \sqrt{9 - 4 \cdot (- 4 n)}}{2 \cdot 4}$

Multiply $- 4$ by $- 4$ .

$m = \frac{3 \pm \sqrt{9 + 16 n}}{2 \cdot 4}$

Multiply $2$ by $4$ .

$m = \frac{3 \pm \sqrt{9 + 16 n}}{8}$

The final answer is the combination of both solutions.

$m = \frac{3 + \sqrt{9 + 16 n}}{8}, \frac{3 - \sqrt{9 + 16 n}}{8}$

Solve for m 4m^2-3m=n

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