Solve for n_2019
n_{2019}=q^{2}+q+1
Solve for q
q=\frac{\sqrt{4n_{2019}-3}-1}{2}
q=\frac{-\sqrt{4n_{2019}-3}-1}{2}\text{, }n_{2019}\geq \frac{3}{4}
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n_{2019}=q^{2}+q+1
Swap sides so that all variable terms are on the left hand side.
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