231=(1/2)n(n-1)

Solution for 231=(1/2)n(n-1) equation:

231=(1/2)n(n-1)

We move all terms to the left:

231-((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))+231=0

We multiply all the terms by the denominator


-((+1+231*2)n(n-1))=0


We calculate terms in parentheses: -((+1+231*2)n(n-1)), so:

(+1+231*2)n(n-1)

We add all the numbers together, and all the variables

463n(n-1)

We multiply parentheses

463n^2-463n

Back to the equation:

-(463n^2-463n)


We get rid of parentheses

-463n^2+463n=0

a = -463; b = 463; c = 0;
Δ = b2-4ac
Δ = 4632-4·(-463)·0
Δ = 214369
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{214369}=463$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(463)-463}{2*-463}=\frac{-926}{-926}
=1
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(463)+463}{2*-463}=\frac{0}{-926}
=0
$