8n=4n(n+1)

Solution for 8n=4n(n+1) equation:

8n=4n(n+1)

We move all terms to the left:

8n-(4n(n+1))=0


We calculate terms in parentheses: -(4n(n+1)), so:

4n(n+1)

We multiply parentheses

4n^2+4n

Back to the equation:

-(4n^2+4n)


We get rid of parentheses

-4n^2+8n-4n=0

We add all the numbers together, and all the variables

-4n^2+4n=0

a = -4; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·(-4)·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4}{2*-4}=\frac{-8}{-8}
=1
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*-4}=\frac{0}{-8}
=0
$