n(n+1)/2=435

Solution for n(n+1)/2=435 equation:

n(n+1)/2=435

We move all terms to the left:

n(n+1)/2-(435)=0

We multiply all the terms by the denominator


n(n+1)-435*2=0

We add all the numbers together, and all the variables

n(n+1)-870=0

We multiply parentheses

n^2+n-870=0

a = 1; b = 1; c = -870;
Δ = b2-4ac
Δ = 12-4·1·(-870)
Δ = 3481
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3481}=59$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-59}{2*1}=\frac{-60}{2}
=-30
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+59}{2*1}=\frac{58}{2}
=29
$