3/4n-1/2=1/8,n=1/4

Solution for 3/4n-1/2=1/8,n=1/4 equation:

3/4n-1/2=1/8.n=1/4

We move all terms to the left:

3/4n-1/2-(1/8.n)=0


Domain of the equation: 4n!=0

n!=0/4

n!=0

n∈R



Domain of the equation: 8.n)!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

3/4n-(+1/8.n)-1/2=0

We get rid of parentheses

3/4n-1/8.n-1/2=0

We calculate fractions


(-256n^2)/64n^2+48n/64n^2+(-16n)/64n^2=0

We multiply all the terms by the denominator


(-256n^2)+48n+(-16n)=0

We get rid of parentheses

-256n^2+48n-16n=0

We add all the numbers together, and all the variables

-256n^2+32n=0

a = -256; b = 32; c = 0;
Δ = b2-4ac
Δ = 322-4·(-256)·0
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-32}{2*-256}=\frac{-64}{-512}
=1/8
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+32}{2*-256}=\frac{0}{-512}
=0
$