3n-1/2n=60

Solution for 3n-1/2n=60 equation:

3n-1/2n=60

We move all terms to the left:

3n-1/2n-(60)=0


Domain of the equation: 2n!=0

n!=0/2

n!=0

n∈R


We multiply all the terms by the denominator


3n*2n-60*2n-1=0

Wy multiply elements

6n^2-120n-1=0

a = 6; b = -120; c = -1;
Δ = b2-4ac
Δ = -1202-4·6·(-1)
Δ = 14424
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:

$\sqrt{\Delta}=\sqrt{14424}=\sqrt{4*3606}=\sqrt{4}*\sqrt{3606}=2\sqrt{3606}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-120)-2\sqrt{3606}}{2*6}=\frac{120-2\sqrt{3606}}{12}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-120)+2\sqrt{3606}}{2*6}=\frac{120+2\sqrt{3606}}{12}
$