45/n=270,n

Solution for 45/n=270,n equation:

45/n=270.n

We move all terms to the left:

45/n-(270.n)=0


Domain of the equation: n!=0

n∈R


We add all the numbers together, and all the variables

45/n-(+270.n)=0

We get rid of parentheses

45/n-270.n=0

We multiply all the terms by the denominator


-(270.n)*n+45=0

We add all the numbers together, and all the variables

-(+270.n)*n+45=0

We multiply parentheses

-270n^2+45=0

a = -270; b = 0; c = +45;
Δ = b2-4ac
Δ = 02-4·(-270)·45
Δ = 48600
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:

$\sqrt{\Delta}=\sqrt{48600}=\sqrt{8100*6}=\sqrt{8100}*\sqrt{6}=90\sqrt{6}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-90\sqrt{6}}{2*-270}=\frac{0-90\sqrt{6}}{-540}
=-\frac{90\sqrt{6}}{-540}
=-\frac{\sqrt{6}}{-6}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+90\sqrt{6}}{2*-270}=\frac{0+90\sqrt{6}}{-540}
=\frac{90\sqrt{6}}{-540}
=\frac{\sqrt{6}}{-6}
$