(n(200/n-20))-20=200

Solution for (n(200/n-20))-20=200 equation:

(n(200/n-20))-20=200

We move all terms to the left:

(n(200/n-20))-20-(200)=0


Domain of the equation: n-20))!=0

n∈R


We add all the numbers together, and all the variables

(n(200/n-20))-220=0

We multiply all the terms by the denominator


(n(200-220*n-20))=0


We calculate terms in parentheses: +(n(200-220*n-20)), so:

n(200-220*n-20)

We add all the numbers together, and all the variables

n(-220n+180)

We multiply parentheses

-220n^2+180n

Back to the equation:

+(-220n^2+180n)


We get rid of parentheses

-220n^2+180n=0

a = -220; b = 180; c = 0;
Δ = b2-4ac
Δ = 1802-4·(-220)·0
Δ = 32400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{32400}=180$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(180)-180}{2*-220}=\frac{-360}{-440}
=9/11
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(180)+180}{2*-220}=\frac{0}{-440}
=0
$