(8/3)n=410

Solution for (8/3)n=410 equation:

(8/3)n=410

We move all terms to the left:

(8/3)n-(410)=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-410=0

We multiply parentheses

8n^2-410=0

a = 8; b = 0; c = -410;
Δ = b2-4ac
Δ = 02-4·8·(-410)
Δ = 13120
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:

$\sqrt{\Delta}=\sqrt{13120}=\sqrt{64*205}=\sqrt{64}*\sqrt{205}=8\sqrt{205}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{205}}{2*8}=\frac{0-8\sqrt{205}}{16}
=-\frac{8\sqrt{205}}{16}
=-\frac{\sqrt{205}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{205}}{2*8}=\frac{0+8\sqrt{205}}{16}
=\frac{8\sqrt{205}}{16}
=\frac{\sqrt{205}}{2}
$