5/6n-3/n-1=7/n

Solution for 5/6n-3/n-1=7/n equation:

5/6n-3/n-1=7/n

We move all terms to the left:

5/6n-3/n-1-(7/n)=0


Domain of the equation: 6n!=0

n!=0/6

n!=0

n∈R



Domain of the equation: n!=0

n∈R



Domain of the equation: n)!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

5/6n-3/n-(+7/n)-1=0

We get rid of parentheses

5/6n-3/n-7/n-1=0

We calculate fractions


5n/6n^2+(-42n-3)/6n^2-1=0

We multiply all the terms by the denominator


5n+(-42n-3)-1*6n^2=0

Wy multiply elements

-6n^2+5n+(-42n-3)=0

We get rid of parentheses

-6n^2+5n-42n-3=0

We add all the numbers together, and all the variables

-6n^2-37n-3=0

a = -6; b = -37; c = -3;
Δ = b2-4ac
Δ = -372-4·(-6)·(-3)
Δ = 1297
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-37)-\sqrt{1297}}{2*-6}=\frac{37-\sqrt{1297}}{-12}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-37)+\sqrt{1297}}{2*-6}=\frac{37+\sqrt{1297}}{-12}
$