n(n+1)=930

Solution for n(n+1)=930 equation:

n(n+1)=930

We move all terms to the left:

n(n+1)-(930)=0

We multiply parentheses

n^2+n-930=0

a = 1; b = 1; c = -930;
Δ = b2-4ac
Δ = 12-4·1·(-930)
Δ = 3721
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3721}=61$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-61}{2*1}=\frac{-62}{2}
=-31
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+61}{2*1}=\frac{60}{2}
=30
$