5/6n=10n=12

Solution for 5/6n=10n=12 equation:

5/6n=10n=12

We move all terms to the left:

5/6n-(10n)=0


Domain of the equation: 6n!=0

n!=0/6

n!=0

n∈R


We add all the numbers together, and all the variables

-10n+5/6n=0

We multiply all the terms by the denominator


-10n*6n+5=0

Wy multiply elements

-60n^2+5=0

a = -60; b = 0; c = +5;
Δ = b2-4ac
Δ = 02-4·(-60)·5
Δ = 1200
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:

$\sqrt{\Delta}=\sqrt{1200}=\sqrt{400*3}=\sqrt{400}*\sqrt{3}=20\sqrt{3}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{3}}{2*-60}=\frac{0-20\sqrt{3}}{-120}
=-\frac{20\sqrt{3}}{-120}
=-\frac{\sqrt{3}}{-6}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{3}}{2*-60}=\frac{0+20\sqrt{3}}{-120}
=\frac{20\sqrt{3}}{-120}
=\frac{\sqrt{3}}{-6}
$