1/4n+8=6n=

Solution for 1/4n+8=6n= equation:

1/4n+8=6n=

We move all terms to the left:

1/4n+8-(6n)=0


Domain of the equation: 4n!=0

n!=0/4

n!=0

n∈R


We add all the numbers together, and all the variables

-6n+1/4n+8=0

We multiply all the terms by the denominator


-6n*4n+8*4n+1=0

Wy multiply elements

-24n^2+32n+1=0

a = -24; b = 32; c = +1;
Δ = b2-4ac
Δ = 322-4·(-24)·1
Δ = 1120
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:

$\sqrt{\Delta}=\sqrt{1120}=\sqrt{16*70}=\sqrt{16}*\sqrt{70}=4\sqrt{70}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-4\sqrt{70}}{2*-24}=\frac{-32-4\sqrt{70}}{-48}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+4\sqrt{70}}{2*-24}=\frac{-32+4\sqrt{70}}{-48}
$