(4+1/3)n=6

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

(4+1/3)n=6

We move all terms to the left:

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


Domain of the equation: 3)n!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

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

We multiply parentheses

n^2+4n-6=0

a = 1; b = 4; c = -6;
Δ = b2-4ac
Δ = 42-4·1·(-6)
Δ = 40
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:

$\sqrt{\Delta}=\sqrt{40}=\sqrt{4*10}=\sqrt{4}*\sqrt{10}=2\sqrt{10}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{10}}{2*1}=\frac{-4-2\sqrt{10}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{10}}{2*1}=\frac{-4+2\sqrt{10}}{2}
$