5/6n+1=2/3n+10

Solution for 5/6n+1=2/3n+10 equation:

5/6n+1=2/3n+10

We move all terms to the left:

5/6n+1-(2/3n+10)=0


Domain of the equation: 6n!=0

n!=0/6

n!=0

n∈R



Domain of the equation: 3n+10)!=0

n∈R


We get rid of parentheses

5/6n-2/3n-10+1=0

We calculate fractions


15n/18n^2+(-12n)/18n^2-10+1=0

We add all the numbers together, and all the variables

15n/18n^2+(-12n)/18n^2-9=0

We multiply all the terms by the denominator


15n+(-12n)-9*18n^2=0

Wy multiply elements

-162n^2+15n+(-12n)=0

We get rid of parentheses

-162n^2+15n-12n=0

We add all the numbers together, and all the variables

-162n^2+3n=0

a = -162; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·(-162)·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*-162}=\frac{-6}{-324}
=1/54
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*-162}=\frac{0}{-324}
=0
$