172.8=180n-360/n

Solution for 172.8=180n-360/n equation:

172.8=180n-360/n

We move all terms to the left:

172.8-(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

-(+180n-360/n)+172.8=0

We get rid of parentheses

-180n+360/n+172.8=0

We multiply all the terms by the denominator


-180n*n+(172.8)*n+360=0

We multiply parentheses

-180n*n+172.8n+360=0

Wy multiply elements

-180n^2+172.8n+360=0

a = -180; b = 172.8; c = +360;
Δ = b2-4ac
Δ = 172.82-4·(-180)·360
Δ = 289059.84
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(172.8)-\sqrt{289059.84}}{2*-180}=\frac{-172.8-\sqrt{289059.84}}{-360}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(172.8)+\sqrt{289059.84}}{2*-180}=\frac{-172.8+\sqrt{289059.84}}{-360}
$