10-5/18n=6+1/6n

Solution for 10-5/18n=6+1/6n equation:

10-5/18n=6+1/6n

We move all terms to the left:

10-5/18n-(6+1/6n)=0


Domain of the equation: 18n!=0

n!=0/18

n!=0

n∈R



Domain of the equation: 6n)!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

-5/18n-(1/6n+6)+10=0

We get rid of parentheses

-5/18n-1/6n-6+10=0

We calculate fractions


(-30n)/108n^2+(-18n)/108n^2-6+10=0

We add all the numbers together, and all the variables

(-30n)/108n^2+(-18n)/108n^2+4=0

We multiply all the terms by the denominator


(-30n)+(-18n)+4*108n^2=0

Wy multiply elements

432n^2+(-30n)+(-18n)=0

We get rid of parentheses

432n^2-30n-18n=0

We add all the numbers together, and all the variables

432n^2-48n=0

a = 432; b = -48; c = 0;
Δ = b2-4ac
Δ = -482-4·432·0
Δ = 2304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2304}=48$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-48}{2*432}=\frac{0}{864}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+48}{2*432}=\frac{96}{864}
=1/9
$