n(n-3)/2=208

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Solution for n(n-3)/2=208 equation:



n(n-3)/2=208
We move all terms to the left:
n(n-3)/2-(208)=0
We multiply all the terms by the denominator
n(n-3)-208*2=0
We add all the numbers together, and all the variables
n(n-3)-416=0
We multiply parentheses
n^2-3n-416=0
a = 1; b = -3; c = -416;
Δ = b2-4ac
Δ = -32-4·1·(-416)
Δ = 1673
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-\sqrt{1673}}{2*1}=\frac{3-\sqrt{1673}}{2} $
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{1673}}{2*1}=\frac{3+\sqrt{1673}}{2} $

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