4/3n+12=n

Solution for 4/3n+12=n equation:

4/3n+12=n

We move all terms to the left:

4/3n+12-(n)=0


Domain of the equation: 3n!=0

n!=0/3

n!=0

n∈R


We add all the numbers together, and all the variables

-1n+4/3n+12=0

We multiply all the terms by the denominator


-1n*3n+12*3n+4=0

Wy multiply elements

-3n^2+36n+4=0

a = -3; b = 36; c = +4;
Δ = b2-4ac
Δ = 362-4·(-3)·4
Δ = 1344
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:

$\sqrt{\Delta}=\sqrt{1344}=\sqrt{64*21}=\sqrt{64}*\sqrt{21}=8\sqrt{21}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-8\sqrt{21}}{2*-3}=\frac{-36-8\sqrt{21}}{-6}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+8\sqrt{21}}{2*-3}=\frac{-36+8\sqrt{21}}{-6}
$