3(n+4)=1/2)6n+4)

Solution for 3(n+4)=1/2)6n+4) equation:

3(n+4)=1/2)6n+4)

We move all terms to the left:

3(n+4)-(1/2)6n+4))=0


Domain of the equation: 2)6n!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

3(n+4)-(+1/2)6n+4))=0

We add all the numbers together, and all the variables

3(n+4)-(+1/2)6n=0

We multiply parentheses

-6n^2+3n+12=0

a = -6; b = 3; c = +12;
Δ = b2-4ac
Δ = 32-4·(-6)·12
Δ = 297
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:

$\sqrt{\Delta}=\sqrt{297}=\sqrt{9*33}=\sqrt{9}*\sqrt{33}=3\sqrt{33}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3\sqrt{33}}{2*-6}=\frac{-3-3\sqrt{33}}{-12}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3\sqrt{33}}{2*-6}=\frac{-3+3\sqrt{33}}{-12}
$