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7n^2+2407n+61800=0
a = 7; b = 2407; c = +61800;
Δ = b2-4ac
Δ = 24072-4·7·61800
Δ = 4063249
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{4063249}=\sqrt{529*7681}=\sqrt{529}*\sqrt{7681}=23\sqrt{7681}$$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2407)-23\sqrt{7681}}{2*7}=\frac{-2407-23\sqrt{7681}}{14} $$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2407)+23\sqrt{7681}}{2*7}=\frac{-2407+23\sqrt{7681}}{14} $
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