C(n)=20-10/n

Solution for C(n)=20-10/n equation:

(C)=20-10/C

We move all terms to the left:

(C)-(20-10/C)=0


Domain of the equation: C)!=0

C!=0/1

C!=0

C∈R


We add all the numbers together, and all the variables

C-(-10/C+20)=0

We get rid of parentheses

C+10/C-20=0

We multiply all the terms by the denominator


C*C-20*C+10=0

We add all the numbers together, and all the variables

-20C+C*C+10=0

Wy multiply elements

C^2-20C+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:
$C_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$C_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

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