10-5/8n=6+1/6n

Solution for 10-5/8n=6+1/6n equation:

10-5/8n=6+1/6n

We move all terms to the left:

10-5/8n-(6+1/6n)=0


Domain of the equation: 8n!=0

n!=0/8

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

-5/8n-(1/6n+6)+10=0

We get rid of parentheses

-5/8n-1/6n-6+10=0

We calculate fractions


(-30n)/48n^2+(-8n)/48n^2-6+10=0

We add all the numbers together, and all the variables

(-30n)/48n^2+(-8n)/48n^2+4=0

We multiply all the terms by the denominator


(-30n)+(-8n)+4*48n^2=0

Wy multiply elements

192n^2+(-30n)+(-8n)=0

We get rid of parentheses

192n^2-30n-8n=0

We add all the numbers together, and all the variables

192n^2-38n=0

a = 192; b = -38; c = 0;
Δ = b2-4ac
Δ = -382-4·192·0
Δ = 1444
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1444}=38$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-38)-38}{2*192}=\frac{0}{384}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-38)+38}{2*192}=\frac{76}{384}
=19/96
$