What are the solutions to the equation (n(n-3))/2 =n ?

The solutions to the equation (n(n-3))/2 =n are n=5,n=0

Find the zeros of (n(n-3))/2 =n

The zeros of (n(n-3))/2 =n are n=5,n=0

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\frac{n ( n - 3 )}{2} = n

n = 5, n = 0

Solution steps

\frac{n ( n - 3 )}{2} = n

Multiply both sides by

2

n (n - 3) = 2 n

Expand

n (n - 3) : n^{2} - 3 n

n^{2} - 3 n = 2 n

Move

2 n

to the left side

n^{2} - 5 n = 0

Solve with the quadratic formula

n_{1, 2} = \frac{- ( - 5 ) \pm ( - 5 ) ^{2} - 4 \cdot 1 \cdot 0}{2 \cdot 1}

(- 5)^{2} - 4 \cdot 1 \cdot 0 = 5

n_{1, 2} = \frac{- ( - 5 ) \pm 5}{2 \cdot 1}

Separate the solutions

n_{1} = \frac{- ( - 5 ) + 5}{2 \cdot 1}, n_{2} = \frac{- ( - 5 ) - 5}{2 \cdot 1}

n = \frac{- ( - 5 ) + 5}{2 \cdot 1} : 5

n = \frac{- ( - 5 ) - 5}{2 \cdot 1} : 0

The solutions to the quadratic equation are:

n = 5, n = 0

\frac{n ( n - 3 )}{2} = 9

(x - 5) (x + 2) = 12

(2 x + 2)^{2} = (2 x - 2)^{2} + (2 x)^{2}

25 x^{2} + 9 = - 30 x

- 2 x^{2} + 8 x - 14

What are the solutions to the equation (n(n-3))/2 =n ?
The solutions to the equation (n(n-3))/2 =n are n=5,n=0
Find the zeros of (n(n-3))/2 =n
The zeros of (n(n-3))/2 =n are n=5,n=0