U(n)=n(n+1)

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



(U)=U(U+1)

We move all terms to the left:

(U)-(U(U+1))=0



We calculate terms in parentheses: -(U(U+1)), so:

U(U+1)

We multiply parentheses

U^2+U

Back to the equation:

-(U^2+U)



We get rid of parentheses

-U^2+U-U=0

We add all the numbers together, and all the variables

-1U^2=0

a = -1; b = 0; c = 0;
Δ = b2-4ac
Δ = 02-4·(-1)·0
Δ = 0
Delta is equal to zero, so there is only one solution to the equation

                              Stosujemy wzór:
$U=\frac{-b}{2a}=\frac{0}{-2}=0$

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