3/14n+1/4=1/7n-1

Solution for 3/14n+1/4=1/7n-1 equation:

3/14n+1/4=1/7n-1

We move all terms to the left:

3/14n+1/4-(1/7n-1)=0


Domain of the equation: 14n!=0

n!=0/14

n!=0

n∈R



Domain of the equation: 7n-1)!=0

n∈R


We get rid of parentheses

3/14n-1/7n+1+1/4=0

We calculate fractions


686n^2/1568n^2+336n/1568n^2+(-224n)/1568n^2+1=0

We multiply all the terms by the denominator


686n^2+336n+(-224n)+1*1568n^2=0

Wy multiply elements

686n^2+1568n^2+336n+(-224n)=0

We get rid of parentheses

686n^2+1568n^2+336n-224n=0

We add all the numbers together, and all the variables

2254n^2+112n=0

a = 2254; b = 112; c = 0;
Δ = b2-4ac
Δ = 1122-4·2254·0
Δ = 12544
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{12544}=112$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(112)-112}{2*2254}=\frac{-224}{4508}
=-8/161
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(112)+112}{2*2254}=\frac{0}{4508}
=0
$