(n-1)(n/2)=45

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Solution for (n-1)(n/2)=45 equation: 


n in (-oo:+oo)

(n/2)*(n-1) = 45 // - 45

(n/2)*(n-1)-45 = 0

1/2*n*(n-1)-45 = 0

1/2*n*(n-1)-45 = 0

1/2*n^2-1/2*n-45 = 0

1/2*n^2-1/2*n-45 = 0

1/2*n^2-1/2*n-45 = 0

DELTA = (-1/2)^2-(-45*1/2*4)

DELTA = 361/4

DELTA > 0

n = ((361/4)^(1/2)+1/2)/(1/2*2) or n = (1/2-(361/4)^(1/2))/(1/2*2)

n = 10 or n = -9

(n+9)*(n-10) = 0

(n+9)*(n-10) = 0

( n+9 )

n+9 = 0 // - 9

n = -9

( n-10 )

n-10 = 0 // + 10

n = 10

n in { -9, 10 }

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