7+5/6n=2/3n

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

7+5/6n=2/3n

We move all terms to the left:

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

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

We get rid of parentheses

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

We calculate fractions


15n/18n^2+(-12n)/18n^2+7=0

We multiply all the terms by the denominator


15n+(-12n)+7*18n^2=0

Wy multiply elements

126n^2+15n+(-12n)=0

We get rid of parentheses

126n^2+15n-12n=0

We add all the numbers together, and all the variables

126n^2+3n=0

a = 126; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·126·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3}{2*126}=\frac{-6}{252}
=-1/42
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*126}=\frac{0}{252}
=0
$