10/n=20-n

Solution for 10/n=20-n equation:

10/n=20-n

We move all terms to the left:

10/n-(20-n)=0


Domain of the equation: n!=0

n∈R


We add all the numbers together, and all the variables

10/n-(-1n+20)=0

We get rid of parentheses

10/n+1n-20=0

We multiply all the terms by the denominator


1n*n-20*n+10=0

We add all the numbers together, and all the variables

-20n+1n*n+10=0

Wy multiply elements

n^2-20n+10=0

a = 1; b = -20; c = +10;
Δ = b2-4ac
Δ = -202-4·1·10
Δ = 360
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:

$\sqrt{\Delta}=\sqrt{360}=\sqrt{36*10}=\sqrt{36}*\sqrt{10}=6\sqrt{10}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-6\sqrt{10}}{2*1}=\frac{20-6\sqrt{10}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+6\sqrt{10}}{2*1}=\frac{20+6\sqrt{10}}{2}
$