8+7/10n=6+1/5n

Solution for 8+7/10n=6+1/5n equation:

8+7/10n=6+1/5n

We move all terms to the left:

8+7/10n-(6+1/5n)=0


Domain of the equation: 10n!=0

n!=0/10

n!=0

n∈R



Domain of the equation: 5n)!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

7/10n-(1/5n+6)+8=0

We get rid of parentheses

7/10n-1/5n-6+8=0

We calculate fractions


35n/50n^2+(-10n)/50n^2-6+8=0

We add all the numbers together, and all the variables

35n/50n^2+(-10n)/50n^2+2=0

We multiply all the terms by the denominator


35n+(-10n)+2*50n^2=0

Wy multiply elements

100n^2+35n+(-10n)=0

We get rid of parentheses

100n^2+35n-10n=0

We add all the numbers together, and all the variables

100n^2+25n=0

a = 100; b = 25; c = 0;
Δ = b2-4ac
Δ = 252-4·100·0
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-25}{2*100}=\frac{-50}{200}
=-1/4
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+25}{2*100}=\frac{0}{200}
=0
$