Solve n^2+7n-3m+6m^2+6m=2n

$${ n }^{ 2 } +7n-3m+6 { m }^{ 2 } +6m = 2n$$

Solve for m (complex solution)

$$m=\frac{\sqrt{9-120n-24n^{2}}}{12}-\frac{1}{4}$$

$$m=-\frac{\sqrt{9-120n-24n^{2}}}{12}-\frac{1}{4}$$

Solve for n (complex solution)

$$n=\frac{\sqrt{25-12m-24m^{2}}-5}{2}$$

$$n=\frac{-\sqrt{25-12m-24m^{2}}-5}{2}$$

Solve for m

$$m=\frac{\sqrt{9-120n-24n^{2}}}{12}-\frac{1}{4}$$

$$m=-\frac{\sqrt{9-120n-24n^{2}}}{12}-\frac{1}{4}\text{, }n\geq -\frac{\sqrt{106}}{4}-\frac{5}{2}\text{ and }n\leq \frac{\sqrt{106}}{4}-\frac{5}{2}$$

Solve for n

$$n=\frac{\sqrt{25-12m-24m^{2}}-5}{2}$$

$$n=\frac{-\sqrt{25-12m-24m^{2}}-5}{2}\text{, }m\geq -\frac{\sqrt{159}}{12}-\frac{1}{4}\text{ and }m\leq \frac{\sqrt{159}}{12}-\frac{1}{4}$$