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n(n-1)=462

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Solution for n(n-1)=462 equation: 



n(n-1)=462

We move all terms to the left:

n(n-1)-(462)=0

We multiply parentheses

n^2-1n-462=0

a = 1; b = -1; c = -462;
Δ = b2-4ac
Δ = -12-4·1·(-462)
Δ = 1849
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}

\sqrt{\Delta}=\sqrt{1849}=43


n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-43}{2*1}=\frac{-42}{2}
=-21



n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+43}{2*1}=\frac{44}{2}
=22

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