1/5n+n=180

Solution for 1/5n+n=180 equation:

1/5n+n=180

We move all terms to the left:

1/5n+n-(180)=0


Domain of the equation: 5n!=0

n!=0/5

n!=0

n∈R


We add all the numbers together, and all the variables

n+1/5n-180=0

We multiply all the terms by the denominator


n*5n-180*5n+1=0

Wy multiply elements

5n^2-900n+1=0

a = 5; b = -900; c = +1;
Δ = b2-4ac
Δ = -9002-4·5·1
Δ = 809980
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:

$\sqrt{\Delta}=\sqrt{809980}=\sqrt{4*202495}=\sqrt{4}*\sqrt{202495}=2\sqrt{202495}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-900)-2\sqrt{202495}}{2*5}=\frac{900-2\sqrt{202495}}{10}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-900)+2\sqrt{202495}}{2*5}=\frac{900+2\sqrt{202495}}{10}
$