420=n(n+1)/2

Solution for 420=n(n+1)/2 equation:

420=n(n+1)/2

We move all terms to the left:

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

We multiply all the terms by the denominator


-(n(n+1)+420*2)=0


We calculate terms in parentheses: -(n(n+1)+420*2), so:

n(n+1)+420*2

We add all the numbers together, and all the variables

n(n+1)+840

We multiply parentheses

n^2+n+840

Back to the equation:

-(n^2+n+840)


We get rid of parentheses

-n^2-n-840=0

We add all the numbers together, and all the variables

-1n^2-1n-840=0

a = -1; b = -1; c = -840;
Δ = b2-4ac
Δ = -12-4·(-1)·(-840)
Δ = -3359
Delta is less than zero, so there is no solution for the equation