21-2n=1/3n

Solution for 21-2n=1/3n equation:

21-2n=1/3n

We move all terms to the left:

21-2n-(1/3n)=0


Domain of the equation: 3n)!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

-2n-(+1/3n)+21=0

We get rid of parentheses

-2n-1/3n+21=0

We multiply all the terms by the denominator


-2n*3n+21*3n-1=0

Wy multiply elements

-6n^2+63n-1=0

a = -6; b = 63; c = -1;
Δ = b2-4ac
Δ = 632-4·(-6)·(-1)
Δ = 3945
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(63)-\sqrt{3945}}{2*-6}=\frac{-63-\sqrt{3945}}{-12}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(63)+\sqrt{3945}}{2*-6}=\frac{-63+\sqrt{3945}}{-12}
$