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100n^2+900n-18800=0
a = 100; b = 900; c = -18800;
Δ = b2-4ac
Δ = 9002-4·100·(-18800)
Δ = 8330000
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}$$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{8330000}=\sqrt{490000*17}=\sqrt{490000}*\sqrt{17}=700\sqrt{17}$$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(900)-700\sqrt{17}}{2*100}=\frac{-900-700\sqrt{17}}{200} $$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(900)+700\sqrt{17}}{2*100}=\frac{-900+700\sqrt{17}}{200} $
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