140n=180n-360/n

Solution for 140n=180n-360/n equation:

140n=180n-360/n

We move all terms to the left:

140n-(180n-360/n)=0


Domain of the equation: n)!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

140n-(+180n-360/n)=0

We get rid of parentheses

140n-180n+360/n=0

We multiply all the terms by the denominator


140n*n-180n*n+360=0

Wy multiply elements

140n^2-180n^2+360=0

We add all the numbers together, and all the variables

-40n^2+360=0

a = -40; b = 0; c = +360;
Δ = b2-4ac
Δ = 02-4·(-40)·360
Δ = 57600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{57600}=240$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-240}{2*-40}=\frac{-240}{-80}
=+3
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+240}{2*-40}=\frac{240}{-80}
=-3
$