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

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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 $

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