0.5n(n+1)=528

Solution for 0.5n(n+1)=528 equation:

0.5n(n+1)=528

We move all terms to the left:

0.5n(n+1)-(528)=0

We multiply parentheses

0n^2+0n-528=0

We add all the numbers together, and all the variables

n^2+n-528=0

a = 1; b = 1; c = -528;
Δ = b2-4ac
Δ = 12-4·1·(-528)
Δ = 2113
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{2113}}{2*1}=\frac{-1-\sqrt{2113}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{2113}}{2*1}=\frac{-1+\sqrt{2113}}{2}
$