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

Evaluate

\frac{n}{2} = n \times \frac{n - 1}{2}

Multiply the terms

\frac{n}{2} = \frac{n ( n - 1 )}{2}

Swap the sides

\frac{n ( n - 1 )}{2} = \frac{n}{2}

Multiply both sides of the equation by LCD

\frac{n ( n - 1 )}{2} \times 2 = \frac{n}{2} \times 2

Simplify the equation

More Steps

n^{2} - n = \frac{n}{2} \times 2

Simplify the equation

n^{2} - n = n

Move the expression to the left side

n^{2} - 2 n = 0

Factor the expression

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n (n - 2) = 0

When the product of factors equals 0,at least one factor is 0

n - 2 = 0 n = 0

Solve the equation for n

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n = 2 n = 0

Solution

n_{1} = 0, n_{2} = 2

Solve the quadratic equation