5/6n-1/2n=7/4

Solution for 5/6n-1/2n=7/4 equation:

5/6n-1/2n=7/4

We move all terms to the left:

5/6n-1/2n-(7/4)=0


Domain of the equation: 6n!=0

n!=0/6

n!=0

n∈R



Domain of the equation: 2n!=0

n!=0/2

n!=0

n∈R


We add all the numbers together, and all the variables

5/6n-1/2n-(+7/4)=0

We get rid of parentheses

5/6n-1/2n-7/4=0

We calculate fractions


(-168n^2)/192n^2+160n/192n^2+(-96n)/192n^2=0

We multiply all the terms by the denominator


(-168n^2)+160n+(-96n)=0

We get rid of parentheses

-168n^2+160n-96n=0

We add all the numbers together, and all the variables

-168n^2+64n=0

a = -168; b = 64; c = 0;
Δ = b2-4ac
Δ = 642-4·(-168)·0
Δ = 4096
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4096}=64$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(64)-64}{2*-168}=\frac{-128}{-336}
=8/21
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(64)+64}{2*-168}=\frac{0}{-336}
=0
$