n(n+1)/3=297

Solution for n(n+1)/3=297 equation:

n(n+1)/3=297

We move all terms to the left:

n(n+1)/3-(297)=0

We multiply all the terms by the denominator


n(n+1)-297*3=0

We add all the numbers together, and all the variables

n(n+1)-891=0

We multiply parentheses

n^2+n-891=0

a = 1; b = 1; c = -891;
Δ = b2-4ac
Δ = 12-4·1·(-891)
Δ = 3565
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{3565}}{2*1}=\frac{-1-\sqrt{3565}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{3565}}{2*1}=\frac{-1+\sqrt{3565}}{2}
$