6/15n=180n=

Solution for 6/15n=180n= equation:

6/15n=180n=

We move all terms to the left:

6/15n-(180n)=0


Domain of the equation: 15n!=0

n!=0/15

n!=0

n∈R


We add all the numbers together, and all the variables

-180n+6/15n=0

We multiply all the terms by the denominator


-180n*15n+6=0

Wy multiply elements

-2700n^2+6=0

a = -2700; b = 0; c = +6;
Δ = b2-4ac
Δ = 02-4·(-2700)·6
Δ = 64800
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:

$\sqrt{\Delta}=\sqrt{64800}=\sqrt{32400*2}=\sqrt{32400}*\sqrt{2}=180\sqrt{2}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-180\sqrt{2}}{2*-2700}=\frac{0-180\sqrt{2}}{-5400}
=-\frac{180\sqrt{2}}{-5400}
=-\frac{\sqrt{2}}{-30}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+180\sqrt{2}}{2*-2700}=\frac{0+180\sqrt{2}}{-5400}
=\frac{180\sqrt{2}}{-5400}
=\frac{\sqrt{2}}{-30}
$