20+1/3n=2n

Solution for 20+1/3n=2n equation:

20+1/3n=2n

We move all terms to the left:

20+1/3n-(2n)=0


Domain of the equation: 3n!=0

n!=0/3

n!=0

n∈R


We add all the numbers together, and all the variables

-2n+1/3n+20=0

We multiply all the terms by the denominator


-2n*3n+20*3n+1=0

Wy multiply elements

-6n^2+60n+1=0

a = -6; b = 60; c = +1;
Δ = b2-4ac
Δ = 602-4·(-6)·1
Δ = 3624
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:

$\sqrt{\Delta}=\sqrt{3624}=\sqrt{4*906}=\sqrt{4}*\sqrt{906}=2\sqrt{906}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-2\sqrt{906}}{2*-6}=\frac{-60-2\sqrt{906}}{-12}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+2\sqrt{906}}{2*-6}=\frac{-60+2\sqrt{906}}{-12}
$