3/6n=14,n=

Solution for 3/6n=14,n= equation:

3/6n=14.n=

We move all terms to the left:

3/6n-(14.n)=0


Domain of the equation: 6n!=0

n!=0/6

n!=0

n∈R


We add all the numbers together, and all the variables

3/6n-(+14.n)=0

We get rid of parentheses

3/6n-14.n=0

We multiply all the terms by the denominator


-(14.n)*6n+3=0

We add all the numbers together, and all the variables

-(+14.n)*6n+3=0

We multiply parentheses

-84n^2+3=0

a = -84; b = 0; c = +3;
Δ = b2-4ac
Δ = 02-4·(-84)·3
Δ = 1008
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1008}=\sqrt{144*7}=\sqrt{144}*\sqrt{7}=12\sqrt{7}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{7}}{2*-84}=\frac{0-12\sqrt{7}}{-168}
=-\frac{12\sqrt{7}}{-168}
=-\frac{\sqrt{7}}{-14}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{7}}{2*-84}=\frac{0+12\sqrt{7}}{-168}
=\frac{12\sqrt{7}}{-168}
=\frac{\sqrt{7}}{-14}
$