2(4n-12)3n=6(n1)

Solution for 2(4n-12)3n=6(n1) equation:

2(4n-12)3n=6(n1)

We move all terms to the left:

2(4n-12)3n-(6(n1))=0

determiningTheFunctionDomain
2(4n-12)3n-6n1=0

We add all the numbers together, and all the variables

-6n+2(4n-12)3n=0

We multiply parentheses

24n^2-6n-72n=0

We add all the numbers together, and all the variables

24n^2-78n=0

a = 24; b = -78; c = 0;
Δ = b2-4ac
Δ = -782-4·24·0
Δ = 6084
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6084}=78$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-78)-78}{2*24}=\frac{0}{48}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-78)+78}{2*24}=\frac{156}{48}
=3+1/4
$