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n^2-n-2000=0
We add all the numbers together, and all the variables
n^2-1n-2000=0
a = 1; b = -1; c = -2000;
Δ = b2-4ac
Δ = -12-4·1·(-2000)
Δ = 8001
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}$$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{8001}=\sqrt{9*889}=\sqrt{9}*\sqrt{889}=3\sqrt{889}$$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-3\sqrt{889}}{2*1}=\frac{1-3\sqrt{889}}{2} $$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+3\sqrt{889}}{2*1}=\frac{1+3\sqrt{889}}{2} $
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