n(n-1)/2=930

Solution for n(n-1)/2=930 equation:

n(n-1)/2=930

We move all terms to the left:

n(n-1)/2-(930)=0

We multiply all the terms by the denominator


n(n-1)-930*2=0

We add all the numbers together, and all the variables

n(n-1)-1860=0

We multiply parentheses

n^2-1n-1860=0

a = 1; b = -1; c = -1860;
Δ = b2-4ac
Δ = -12-4·1·(-1860)
Δ = 7441
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{7441}}{2*1}=\frac{1-\sqrt{7441}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{7441}}{2*1}=\frac{1+\sqrt{7441}}{2}
$