2/n=n/5n+12

Solution for 2/n=n/5n+12 equation:

2/n=n/5n+12

We move all terms to the left:

2/n-(n/5n+12)=0


Domain of the equation: n!=0

n∈R



Domain of the equation: 5n+12)!=0

n∈R


We get rid of parentheses

2/n-n/5n-12=0

We calculate fractions


(-1n^2)/5n^2+10n/5n^2-12=0

We multiply all the terms by the denominator


(-1n^2)+10n-12*5n^2=0

Wy multiply elements

(-1n^2)-60n^2+10n=0

We get rid of parentheses

-1n^2-60n^2+10n=0

We add all the numbers together, and all the variables

-61n^2+10n=0

a = -61; b = 10; c = 0;
Δ = b2-4ac
Δ = 102-4·(-61)·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10}{2*-61}=\frac{-20}{-122}
=10/61
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10}{2*-61}=\frac{0}{-122}
=0
$