1/2n+4n=12

Solution for 1/2n+4n=12 equation:

1/2n+4n=12

We move all terms to the left:

1/2n+4n-(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

4n+1/2n-12=0

We multiply all the terms by the denominator


4n*2n-12*2n+1=0

Wy multiply elements

8n^2-24n+1=0

a = 8; b = -24; c = +1;
Δ = b2-4ac
Δ = -242-4·8·1
Δ = 544
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:

$\sqrt{\Delta}=\sqrt{544}=\sqrt{16*34}=\sqrt{16}*\sqrt{34}=4\sqrt{34}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-4\sqrt{34}}{2*8}=\frac{24-4\sqrt{34}}{16}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+4\sqrt{34}}{2*8}=\frac{24+4\sqrt{34}}{16}
$