(x)(x-1)/2=66

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Solution for (x)(x-1)/2=66 equation: 


x in (-oo:+oo)

(x*(x-1))/2 = 66 // - 66

(x*(x-1))/2-66 = 0

(x*(x-1))/2+(-66*2)/2 = 0

x*(x-1)-66*2 = 0

x^2-x-132 = 0

x^2-x-132 = 0

x^2-x-132 = 0

DELTA = (-1)^2-(-132*1*4)

DELTA = 529

DELTA > 0

x = (529^(1/2)+1)/(1*2) or x = (1-529^(1/2))/(1*2)

x = 12 or x = -11

(x+11)*(x-12) = 0

((x+11)*(x-12))/2 = 0

((x+11)*(x-12))/2 = 0 // * 2

(x+11)*(x-12) = 0

( x+11 )

x+11 = 0 // - 11

x = -11

( x-12 )

x-12 = 0 // + 12

x = 12

x in { -11, 12 }

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