4/n=n/9n=

Solution for 4/n=n/9n= equation:

4/n=n/9n=

We move all terms to the left:

4/n-(n/9n)=0


Domain of the equation: n!=0

n∈R



Domain of the equation: 9n)!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

4/n-(+n/9n)=0

We get rid of parentheses

4/n-n/9n=0

We calculate fractions


(-1n^2)/9n^2+36n/9n^2=0

We multiply all the terms by the denominator


(-1n^2)+36n=0

We get rid of parentheses

-1n^2+36n=0

a = -1; b = 36; c = 0;
Δ = b2-4ac
Δ = 362-4·(-1)·0
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-36}{2*-1}=\frac{-72}{-2}
=+36
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+36}{2*-1}=\frac{0}{-2}
=0
$