What are the solutions to the equation (n(n+1))/2 =210 ?

The solutions to the equation (n(n+1))/2 =210 are n=20,n=-21

Find the zeros of (n(n+1))/2 =210

The zeros of (n(n+1))/2 =210 are n=20,n=-21

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\frac{n ( n + 1 )}{2} = 210

n = 20, n = - 21

Solution steps

\frac{n ( n + 1 )}{2} = 210

Multiply both sides by

2

n (n + 1) = 420

Expand

n (n + 1) : n^{2} + n

n^{2} + n = 420

Move

420

to the left side

n^{2} + n - 420 = 0

Solve with the quadratic formula

n_{1, 2} = \frac{- 1 \pm 1 ^{2} - 4 \cdot 1 \cdot ( - 420 )}{2 \cdot 1}

1^{2} - 4 \cdot 1 \cdot (- 420) = 41

n_{1, 2} = \frac{- 1 \pm 41}{2 \cdot 1}

Separate the solutions

n_{1} = \frac{- 1 + 41}{2 \cdot 1}, n_{2} = \frac{- 1 - 41}{2 \cdot 1}

n = \frac{- 1 + 41}{2 \cdot 1} : 20

n = \frac{- 1 - 41}{2 \cdot 1} : - 21

The solutions to the quadratic equation are:

n = 20, n = - 21

\frac{2}{2 - x} \leq \frac{4}{x}

\frac{14}{51} \cdot \frac{3}{4}

4 (2 x - 2) = 8

x^{2} = \frac{1}{9}

- x^{2} + 8 x + 4 = 0

What are the solutions to the equation (n(n+1))/2 =210 ?
The solutions to the equation (n(n+1))/2 =210 are n=20,n=-21
Find the zeros of (n(n+1))/2 =210
The zeros of (n(n+1))/2 =210 are n=20,n=-21