5/8*n=16

Solution for 5/8*n=16 equation:

5/8*n=16

We move all terms to the left:

5/8*n-(16)=0


Domain of the equation: 8*n!=0

n!=0/1

n!=0

n∈R


We multiply all the terms by the denominator


-16*8*n+5=0

Wy multiply elements

-128n*n+5=0

Wy multiply elements

-128n^2+5=0

a = -128; b = 0; c = +5;
Δ = b2-4ac
Δ = 02-4·(-128)·5
Δ = 2560
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:

$\sqrt{\Delta}=\sqrt{2560}=\sqrt{256*10}=\sqrt{256}*\sqrt{10}=16\sqrt{10}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16\sqrt{10}}{2*-128}=\frac{0-16\sqrt{10}}{-256}
=-\frac{16\sqrt{10}}{-256}
=-\frac{\sqrt{10}}{-16}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16\sqrt{10}}{2*-128}=\frac{0+16\sqrt{10}}{-256}
=\frac{16\sqrt{10}}{-256}
=\frac{\sqrt{10}}{-16}
$