102=(1/2)n(n-1)

Solution for 102=(1/2)n(n-1) equation:

102=(1/2)n(n-1)

We move all terms to the left:

102-((1/2)n(n-1))=0


Domain of the equation: 2)n(n-1))!=0

n∈R


We add all the numbers together, and all the variables

-((+1/2)n(n-1))+102=0

We multiply all the terms by the denominator


-((+1+102*2)n(n-1))=0


We calculate terms in parentheses: -((+1+102*2)n(n-1)), so:

(+1+102*2)n(n-1)

We add all the numbers together, and all the variables

205n(n-1)

We multiply parentheses

205n^2-205n

Back to the equation:

-(205n^2-205n)


We get rid of parentheses

-205n^2+205n=0

a = -205; b = 205; c = 0;
Δ = b2-4ac
Δ = 2052-4·(-205)·0
Δ = 42025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{42025}=205$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(205)-205}{2*-205}=\frac{-410}{-410}
=1
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(205)+205}{2*-205}=\frac{0}{-410}
=0
$