84/n=6n=

Solution for 84/n=6n= equation:

84/n=6n=

We move all terms to the left:

84/n-(6n)=0


Domain of the equation: n!=0

n∈R


We add all the numbers together, and all the variables

-6n+84/n=0

We multiply all the terms by the denominator


-6n*n+84=0

Wy multiply elements

-6n^2+84=0

a = -6; b = 0; c = +84;
Δ = b2-4ac
Δ = 02-4·(-6)·84
Δ = 2016
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:

$\sqrt{\Delta}=\sqrt{2016}=\sqrt{144*14}=\sqrt{144}*\sqrt{14}=12\sqrt{14}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{14}}{2*-6}=\frac{0-12\sqrt{14}}{-12}
=-\frac{12\sqrt{14}}{-12}
=-\frac{\sqrt{14}}{-1}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{14}}{2*-6}=\frac{0+12\sqrt{14}}{-12}
=\frac{12\sqrt{14}}{-12}
=\frac{\sqrt{14}}{-1}
$