1/7n+2=3/14n-1

Solution for 1/7n+2=3/14n-1 equation:

1/7n+2=3/14n-1

We move all terms to the left:

1/7n+2-(3/14n-1)=0


Domain of the equation: 7n!=0

n!=0/7

n!=0

n∈R



Domain of the equation: 14n-1)!=0

n∈R


We get rid of parentheses

1/7n-3/14n+1+2=0

We calculate fractions


14n/98n^2+(-21n)/98n^2+1+2=0

We add all the numbers together, and all the variables

14n/98n^2+(-21n)/98n^2+3=0

We multiply all the terms by the denominator


14n+(-21n)+3*98n^2=0

Wy multiply elements

294n^2+14n+(-21n)=0

We get rid of parentheses

294n^2+14n-21n=0

We add all the numbers together, and all the variables

294n^2-7n=0

a = 294; b = -7; c = 0;
Δ = b2-4ac
Δ = -72-4·294·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-7}{2*294}=\frac{0}{588}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+7}{2*294}=\frac{14}{588}
=1/42
$