n/4n+2n=12

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

n/4n+2n=12

We move all terms to the left:

n/4n+2n-(12)=0


Domain of the equation: 4n!=0

n!=0/4

n!=0

n∈R


We add all the numbers together, and all the variables

2n+n/4n-12=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

8n^2+n-48n=0

We add all the numbers together, and all the variables

8n^2-47n=0

a = 8; b = -47; c = 0;
Δ = b2-4ac
Δ = -472-4·8·0
Δ = 2209
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2209}=47$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-47)-47}{2*8}=\frac{0}{16}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-47)+47}{2*8}=\frac{94}{16}
=5+7/8
$