-1/2n+1/4n=1/8

Solution for -1/2n+1/4n=1/8 equation:

-1/2n+1/4n=1/8

We move all terms to the left:

-1/2n+1/4n-(1/8)=0


Domain of the equation: 2n!=0

n!=0/2

n!=0

n∈R



Domain of the equation: 4n!=0

n!=0/4

n!=0

n∈R


We add all the numbers together, and all the variables

-1/2n+1/4n-(+1/8)=0

We get rid of parentheses

-1/2n+1/4n-1/8=0

We calculate fractions


(-32n^2)/512n^2+(-256n)/512n^2+128n/512n^2=0

We multiply all the terms by the denominator


(-32n^2)+(-256n)+128n=0

We add all the numbers together, and all the variables

(-32n^2)+128n+(-256n)=0

We get rid of parentheses

-32n^2+128n-256n=0

We add all the numbers together, and all the variables

-32n^2-128n=0

a = -32; b = -128; c = 0;
Δ = b2-4ac
Δ = -1282-4·(-32)·0
Δ = 16384
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16384}=128$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-128)-128}{2*-32}=\frac{0}{-64}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-128)+128}{2*-32}=\frac{256}{-64}
=-4
$