7n=84/n

Solution for 7n=84/n equation:

7n=84/n

We move all terms to the left:

7n-(84/n)=0


Domain of the equation: n)!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

7n-(+84/n)=0

We get rid of parentheses

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}
=-2\sqrt{3}
$
$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}
=2\sqrt{3}
$