7/6n=2+5/3n

Solution for 7/6n=2+5/3n equation:

7/6n=2+5/3n

We move all terms to the left:

7/6n-(2+5/3n)=0


Domain of the equation: 6n!=0

n!=0/6

n!=0

n∈R



Domain of the equation: 3n)!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

7/6n-(5/3n+2)=0

We get rid of parentheses

7/6n-5/3n-2=0

We calculate fractions


21n/18n^2+(-30n)/18n^2-2=0

We multiply all the terms by the denominator


21n+(-30n)-2*18n^2=0

Wy multiply elements

-36n^2+21n+(-30n)=0

We get rid of parentheses

-36n^2+21n-30n=0

We add all the numbers together, and all the variables

-36n^2-9n=0

a = -36; b = -9; c = 0;
Δ = b2-4ac
Δ = -92-4·(-36)·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-9}{2*-36}=\frac{0}{-72}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+9}{2*-36}=\frac{18}{-72}
=-1/4
$