c-0.1c=c(1-0.1c)

Solution for c-0.1c=c(1-0.1c) equation:

c-0.1c=c(1-0.1c)

We move all terms to the left:

c-0.1c-(c(1-0.1c))=0

We add all the numbers together, and all the variables

c-0.1c-(c(-0.1c+1))=0

We add all the numbers together, and all the variables

0.9c-(c(-0.1c+1))=0


We calculate terms in parentheses: -(c(-0.1c+1)), so:

c(-0.1c+1)

We multiply parentheses

0c^2+c

We add all the numbers together, and all the variables

c^2+c

Back to the equation:

-(c^2+c)


We get rid of parentheses

-c^2+0.9c-c=0

We add all the numbers together, and all the variables

-1c^2-0.1c=0

a = -1; b = -0.1; c = 0;
Δ = b2-4ac
Δ = -0.12-4·(-1)·0
Δ = 0.01
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-0.1)-\sqrt{0.01}}{2*-1}=\frac{0.1-\sqrt{0.01}}{-2}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.1)+\sqrt{0.01}}{2*-1}=\frac{0.1+\sqrt{0.01}}{-2}
$