n/2n-4=-4n+8

Solution for n/2n-4=-4n+8 equation:

n/2n-4=-4n+8

We move all terms to the left:

n/2n-4-(-4n+8)=0


Domain of the equation: 2n!=0

n!=0/2

n!=0

n∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

8n^2+n-16n-8n=0

We add all the numbers together, and all the variables

8n^2-23n=0

a = 8; b = -23; c = 0;
Δ = b2-4ac
Δ = -232-4·8·0
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-23}{2*8}=\frac{0}{16}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+23}{2*8}=\frac{46}{16}
=2+7/8
$