x*(x+1)/2=453

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Solution for x*(x+1)/2=453 equation: 


x in (-oo:+oo)

(x*(x+1))/2 = 453 // - 453

(x*(x+1))/2-453 = 0

(x*(x+1))/2+(-453*2)/2 = 0

x*(x+1)-453*2 = 0

x^2+x-906 = 0

x^2+x-906 = 0

x^2+x-906 = 0

DELTA = 1^2-(-906*1*4)

DELTA = 3625

DELTA > 0

x = (3625^(1/2)-1)/(1*2) or x = (-3625^(1/2)-1)/(1*2)

x = (5*145^(1/2)-1)/2 or x = (-5*145^(1/2)-1)/2

(x-((-5*145^(1/2)-1)/2))*(x-((5*145^(1/2)-1)/2)) = 0

((x-((-5*145^(1/2)-1)/2))*(x-((5*145^(1/2)-1)/2)))/2 = 0

((x-((-5*145^(1/2)-1)/2))*(x-((5*145^(1/2)-1)/2)))/2 = 0 // * 2

(x-((-5*145^(1/2)-1)/2))*(x-((5*145^(1/2)-1)/2)) = 0

( x-((-5*145^(1/2)-1)/2) )

x-((-5*145^(1/2)-1)/2) = 0 // + (-5*145^(1/2)-1)/2

x = (-5*145^(1/2)-1)/2

( x-((5*145^(1/2)-1)/2) )

x-((5*145^(1/2)-1)/2) = 0 // + (5*145^(1/2)-1)/2

x = (5*145^(1/2)-1)/2

x in { (-5*145^(1/2)-1)/2, (5*145^(1/2)-1)/2 }

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