x*(x+1)/2=100

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Solution for x*(x+1)/2=100 equation: 


x in (-oo:+oo)

(x*(x+1))/2 = 100 // - 100

(x*(x+1))/2-100 = 0

(x*(x+1))/2+(-100*2)/2 = 0

x*(x+1)-100*2 = 0

x^2+x-200 = 0

x^2+x-200 = 0

x^2+x-200 = 0

DELTA = 1^2-(-200*1*4)

DELTA = 801

DELTA > 0

x = (801^(1/2)-1)/(1*2) or x = (-801^(1/2)-1)/(1*2)

x = (3*89^(1/2)-1)/2 or x = (-3*89^(1/2)-1)/2

(x-((-3*89^(1/2)-1)/2))*(x-((3*89^(1/2)-1)/2)) = 0

((x-((-3*89^(1/2)-1)/2))*(x-((3*89^(1/2)-1)/2)))/2 = 0

((x-((-3*89^(1/2)-1)/2))*(x-((3*89^(1/2)-1)/2)))/2 = 0 // * 2

(x-((-3*89^(1/2)-1)/2))*(x-((3*89^(1/2)-1)/2)) = 0

( x-((-3*89^(1/2)-1)/2) )

x-((-3*89^(1/2)-1)/2) = 0 // + (-3*89^(1/2)-1)/2

x = (-3*89^(1/2)-1)/2

( x-((3*89^(1/2)-1)/2) )

x-((3*89^(1/2)-1)/2) = 0 // + (3*89^(1/2)-1)/2

x = (3*89^(1/2)-1)/2

x in { (-3*89^(1/2)-1)/2, (3*89^(1/2)-1)/2 }

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