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8n^2+18n-2000=0
a = 8; b = 18; c = -2000;
Δ = b2-4ac
Δ = 182-4·8·(-2000)
Δ = 64324
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}$$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{64324}=\sqrt{4*16081}=\sqrt{4}*\sqrt{16081}=2\sqrt{16081}$$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{16081}}{2*8}=\frac{-18-2\sqrt{16081}}{16} $$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{16081}}{2*8}=\frac{-18+2\sqrt{16081}}{16} $
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