Solve 225/n+225/n+15+225/n+30+225/n+45=frac{77}{4}

$$\frac { 225 } { n } + \frac { 225 } { n + 15 } + \frac { 225 } { n + 30 } + \frac { 225 } { n + 45 } = \frac { 77 } { 4 }$$

Solve for n

$$n=\frac{10\left(\sqrt{21487}\cos(\frac{\arccos(\frac{52550\sqrt{21487}}{461691169})}{3})-188\right)}{77}\approx -7.876426125$$

$$n=30$$

$$n=\frac{5\left(-\sqrt{21487}\cos(\frac{\arccos(\frac{52550\sqrt{21487}}{461691169})}{3})-\sqrt{64461}\sin(\frac{\arccos(\frac{52550\sqrt{21487}}{461691169})}{3})-376\right)}{77}\approx -40.848865404$$

$$n=\frac{5\left(\sqrt{64461}\sin(\frac{\arccos(\frac{52550\sqrt{21487}}{461691169})}{3})-\sqrt{21487}\cos(\frac{\arccos(\frac{52550\sqrt{21487}}{461691169})}{3})-376\right)}{77}\approx -24.521461718$$