50/n=2n

Solution for 50/n=2n equation:

50/n=2n

We move all terms to the left:

50/n-(2n)=0


Domain of the equation: n!=0

n∈R


We add all the numbers together, and all the variables

-2n+50/n=0

We multiply all the terms by the denominator


-2n*n+50=0

Wy multiply elements

-2n^2+50=0

a = -2; b = 0; c = +50;
Δ = b2-4ac
Δ = 02-4·(-2)·50
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20}{2*-2}=\frac{-20}{-4}
=+5
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20}{2*-2}=\frac{20}{-4}
=-5
$