6(3n)=12/3n

Solution for 6(3n)=12/3n equation:

6(3n)=12/3n

We move all terms to the left:

6(3n)-(12/3n)=0


Domain of the equation: 3n)!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

63n-(+12/3n)=0

We get rid of parentheses

63n-12/3n=0

We multiply all the terms by the denominator


63n*3n-12=0

Wy multiply elements

189n^2-12=0

a = 189; b = 0; c = -12;
Δ = b2-4ac
Δ = 02-4·189·(-12)
Δ = 9072
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:

$\sqrt{\Delta}=\sqrt{9072}=\sqrt{1296*7}=\sqrt{1296}*\sqrt{7}=36\sqrt{7}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-36\sqrt{7}}{2*189}=\frac{0-36\sqrt{7}}{378}
=-\frac{36\sqrt{7}}{378}
=-\frac{2\sqrt{7}}{21}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+36\sqrt{7}}{2*189}=\frac{0+36\sqrt{7}}{378}
=\frac{36\sqrt{7}}{378}
=\frac{2\sqrt{7}}{21}
$