70/6n=n

Solution for 70/6n=n equation:

70/6n=n

We move all terms to the left:

70/6n-(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

-1n+70/6n=0

We multiply all the terms by the denominator


-1n*6n+70=0

Wy multiply elements

-6n^2+70=0

a = -6; b = 0; c = +70;
Δ = b2-4ac
Δ = 02-4·(-6)·70
Δ = 1680
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:

$\sqrt{\Delta}=\sqrt{1680}=\sqrt{16*105}=\sqrt{16}*\sqrt{105}=4\sqrt{105}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{105}}{2*-6}=\frac{0-4\sqrt{105}}{-12}
=-\frac{4\sqrt{105}}{-12}
=-\frac{\sqrt{105}}{-3}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{105}}{2*-6}=\frac{0+4\sqrt{105}}{-12}
=\frac{4\sqrt{105}}{-12}
=\frac{\sqrt{105}}{-3}
$