4/6n=4-n

Solution for 4/6n=4-n equation:

4/6n=4-n

We move all terms to the left:

4/6n-(4-n)=0


Domain of the equation: 6n!=0

n!=0/6

n!=0

n∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

4/6n+1n-4=0

We multiply all the terms by the denominator


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

Wy multiply elements

6n^2-24n+4=0

a = 6; b = -24; c = +4;
Δ = b2-4ac
Δ = -242-4·6·4
Δ = 480
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:

$\sqrt{\Delta}=\sqrt{480}=\sqrt{16*30}=\sqrt{16}*\sqrt{30}=4\sqrt{30}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-4\sqrt{30}}{2*6}=\frac{24-4\sqrt{30}}{12}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+4\sqrt{30}}{2*6}=\frac{24+4\sqrt{30}}{12}
$