2n-3-1/2n=12

Solution for 2n-3-1/2n=12 equation:

2n-3-1/2n=12

We move all terms to the left:

2n-3-1/2n-(12)=0


Domain of the equation: 2n!=0

n!=0/2

n!=0

n∈R


We add all the numbers together, and all the variables

2n-1/2n-15=0

We multiply all the terms by the denominator


2n*2n-15*2n-1=0

Wy multiply elements

4n^2-30n-1=0

a = 4; b = -30; c = -1;
Δ = b2-4ac
Δ = -302-4·4·(-1)
Δ = 916
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:

$\sqrt{\Delta}=\sqrt{916}=\sqrt{4*229}=\sqrt{4}*\sqrt{229}=2\sqrt{229}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{229}}{2*4}=\frac{30-2\sqrt{229}}{8}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{229}}{2*4}=\frac{30+2\sqrt{229}}{8}
$