Solve for t (complex solution)
t=\frac{\sqrt{15}\left(35-N\right)^{-\frac{1}{2}}\left(-\sqrt{15\left(35-N\right)}-300i\right)}{30}
t=\frac{\sqrt{15}\left(35-N\right)^{-\frac{1}{2}}\left(-\sqrt{15\left(35-N\right)}+300i\right)}{30}\text{, }N\neq 35
Solve for N
N=\frac{5\left(28t^{2}+28t+1207\right)}{\left(2t+1\right)^{2}}
t\neq -\frac{1}{2}
Solve for t
t=-\frac{1}{2}+10\sqrt{-\frac{15}{35-N}}
t=-\frac{1}{2}-10\sqrt{-\frac{15}{35-N}}\text{, }N>35
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