84/n=7n

Solution for 84/n=7n equation:

84/n=7n

We move all terms to the left:

84/n-(7n)=0


Domain of the equation: n!=0

n∈R


We add all the numbers together, and all the variables

-7n+84/n=0

We multiply all the terms by the denominator


-7n*n+84=0

Wy multiply elements

-7n^2+84=0

a = -7; b = 0; c = +84;
Δ = b2-4ac
Δ = 02-4·(-7)·84
Δ = 2352
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:

$\sqrt{\Delta}=\sqrt{2352}=\sqrt{784*3}=\sqrt{784}*\sqrt{3}=28\sqrt{3}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-28\sqrt{3}}{2*-7}=\frac{0-28\sqrt{3}}{-14}
=-\frac{28\sqrt{3}}{-14}
=-\frac{2\sqrt{3}}{-1}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+28\sqrt{3}}{2*-7}=\frac{0+28\sqrt{3}}{-14}
=\frac{28\sqrt{3}}{-14}
=\frac{2\sqrt{3}}{-1}
$