(8/3)n-8-3=5

Solution for (8/3)n-8-3=5 equation:

(8/3)n-8-3=5

We move all terms to the left:

(8/3)n-8-3-(5)=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

(+8/3)n-8-3-5=0

We add all the numbers together, and all the variables

(+8/3)n-16=0

We multiply parentheses

8n^2-16=0

a = 8; b = 0; c = -16;
Δ = b2-4ac
Δ = 02-4·8·(-16)
Δ = 512
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:

$\sqrt{\Delta}=\sqrt{512}=\sqrt{256*2}=\sqrt{256}*\sqrt{2}=16\sqrt{2}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16\sqrt{2}}{2*8}=\frac{0-16\sqrt{2}}{16}
=-\frac{16\sqrt{2}}{16}
=-\sqrt{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16\sqrt{2}}{2*8}=\frac{0+16\sqrt{2}}{16}
=\frac{16\sqrt{2}}{16}
=\sqrt{2}
$