1/2n-6=8n

Solution for 1/2n-6=8n equation:

1/2n-6=8n

We move all terms to the left:

1/2n-6-(8n)=0


Domain of the equation: 2n!=0

n!=0/2

n!=0

n∈R


We add all the numbers together, and all the variables

-8n+1/2n-6=0

We multiply all the terms by the denominator


-8n*2n-6*2n+1=0

Wy multiply elements

-16n^2-12n+1=0

a = -16; b = -12; c = +1;
Δ = b2-4ac
Δ = -122-4·(-16)·1
Δ = 208
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:

$\sqrt{\Delta}=\sqrt{208}=\sqrt{16*13}=\sqrt{16}*\sqrt{13}=4\sqrt{13}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{13}}{2*-16}=\frac{12-4\sqrt{13}}{-32}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{13}}{2*-16}=\frac{12+4\sqrt{13}}{-32}
$