1/7n-1=7/8n-2

Solution for 1/7n-1=7/8n-2 equation:

1/7n-1=7/8n-2

We move all terms to the left:

1/7n-1-(7/8n-2)=0


Domain of the equation: 7n!=0

n!=0/7

n!=0

n∈R



Domain of the equation: 8n-2)!=0

n∈R


We get rid of parentheses

1/7n-7/8n+2-1=0

We calculate fractions


8n/56n^2+(-49n)/56n^2+2-1=0

We add all the numbers together, and all the variables

8n/56n^2+(-49n)/56n^2+1=0

We multiply all the terms by the denominator


8n+(-49n)+1*56n^2=0

Wy multiply elements

56n^2+8n+(-49n)=0

We get rid of parentheses

56n^2+8n-49n=0

We add all the numbers together, and all the variables

56n^2-41n=0

a = 56; b = -41; c = 0;
Δ = b2-4ac
Δ = -412-4·56·0
Δ = 1681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1681}=41$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-41)-41}{2*56}=\frac{0}{112}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-41)+41}{2*56}=\frac{82}{112}
=41/56
$