3(n+4)=1/2n

Solution for 3(n+4)=1/2n equation:

3(n+4)=1/2n

We move all terms to the left:

3(n+4)-(1/2n)=0


Domain of the equation: 2n)!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

3(n+4)-(+1/2n)=0

We multiply parentheses

3n-(+1/2n)+12=0

We get rid of parentheses

3n-1/2n+12=0

We multiply all the terms by the denominator


3n*2n+12*2n-1=0

Wy multiply elements

6n^2+24n-1=0

a = 6; b = 24; c = -1;
Δ = b2-4ac
Δ = 242-4·6·(-1)
Δ = 600
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:

$\sqrt{\Delta}=\sqrt{600}=\sqrt{100*6}=\sqrt{100}*\sqrt{6}=10\sqrt{6}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-10\sqrt{6}}{2*6}=\frac{-24-10\sqrt{6}}{12}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+10\sqrt{6}}{2*6}=\frac{-24+10\sqrt{6}}{12}
$