171=(n(n+1))/2

Solution for 171=(n(n+1))/2 equation:

171=(n(n+1))/2

We move all terms to the left:

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

We multiply all the terms by the denominator


-((n(n+1))+171*2)=0


We calculate terms in parentheses: -((n(n+1))+171*2), so:

(n(n+1))+171*2

We add all the numbers together, and all the variables

(n(n+1))+342


We calculate terms in parentheses: +(n(n+1)), so:

n(n+1)

We multiply parentheses

n^2+n

Back to the equation:

+(n^2+n)


We get rid of parentheses

n^2+n+342

Back to the equation:

-(n^2+n+342)


We get rid of parentheses

-n^2-n-342=0

We add all the numbers together, and all the variables

-1n^2-1n-342=0

a = -1; b = -1; c = -342;
Δ = b2-4ac
Δ = -12-4·(-1)·(-342)
Δ = -1367
Delta is less than zero, so there is no solution for the equation