4/n=n-9/n

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

4/n=n-9/n

We move all terms to the left:

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


Domain of the equation: n!=0

n∈R



Domain of the equation: n)!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

4/n-n+9/n=0

We multiply all the terms by the denominator


-n*n+4+9=0

We add all the numbers together, and all the variables

-n*n+13=0

Wy multiply elements

-1n^2+13=0

a = -1; b = 0; c = +13;
Δ = b2-4ac
Δ = 02-4·(-1)·13
Δ = 52
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:

$\sqrt{\Delta}=\sqrt{52}=\sqrt{4*13}=\sqrt{4}*\sqrt{13}=2\sqrt{13}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{13}}{2*-1}=\frac{0-2\sqrt{13}}{-2}
=-\frac{2\sqrt{13}}{-2}
=-\frac{\sqrt{13}}{-1}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{13}}{2*-1}=\frac{0+2\sqrt{13}}{-2}
=\frac{2\sqrt{13}}{-2}
=\frac{\sqrt{13}}{-1}
$