n(n-3)/2=n

Solution for n(n-3)/2=n equation:

n(n-3)/2=n

We move all terms to the left:

n(n-3)/2-(n)=0

We add all the numbers together, and all the variables

-1n+n(n-3)/2=0

We multiply all the terms by the denominator


-1n*2+n(n-3)=0

We multiply parentheses

n^2-1n*2-3n=0

Wy multiply elements

n^2-2n-3n=0

We add all the numbers together, and all the variables

n^2-5n=0

a = 1; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·1·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5}{2*1}=\frac{0}{2}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*1}=\frac{10}{2}
=5
$