55=n*(1+n)/2

Solution for 55=n*(1+n)/2 equation:

55=n(1+n)/2

We move all terms to the left:

55-(n(1+n)/2)=0

We add all the numbers together, and all the variables

-(n(n+1)/2)+55=0

We multiply all the terms by the denominator


-(n(n+1)+55*2)=0


We calculate terms in parentheses: -(n(n+1)+55*2), so:

n(n+1)+55*2

We add all the numbers together, and all the variables

n(n+1)+110

We multiply parentheses

n^2+n+110

Back to the equation:

-(n^2+n+110)


We get rid of parentheses

-n^2-n-110=0

We add all the numbers together, and all the variables

-1n^2-1n-110=0

a = -1; b = -1; c = -110;
Δ = b2-4ac
Δ = -12-4·(-1)·(-110)
Δ = -439
Delta is less than zero, so there is no solution for the equation