c(2)=c(2-1)+10

Solution for c(2)=c(2-1)+10 equation:

c(2)=c(2-1)+10

We move all terms to the left:

c(2)-(c(2-1)+10)=0

We add all the numbers together, and all the variables

c2-(c1+10)=0

We add all the numbers together, and all the variables

c^2-(c1+10)=0

We get rid of parentheses

c^2-c1-10=0

We add all the numbers together, and all the variables

c^2-1c-10=0

a = 1; b = -1; c = -10;
Δ = b2-4ac
Δ = -12-4·1·(-10)
Δ = 41
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{-(-1)-\sqrt{41}}{2*1}=\frac{1-\sqrt{41}}{2}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{41}}{2*1}=\frac{1+\sqrt{41}}{2}
$