64/n=n

Solution for 64/n=n equation:

64/n=n

We move all terms to the left:

64/n-(n)=0


Domain of the equation: n!=0

n∈R


We add all the numbers together, and all the variables

-1n+64/n=0

We multiply all the terms by the denominator


-1n*n+64=0

Wy multiply elements

-1n^2+64=0

a = -1; b = 0; c = +64;
Δ = b2-4ac
Δ = 02-4·(-1)·64
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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