f(2)=2f(2-1)+2

Solution for f(2)=2f(2-1)+2 equation:

f(2)=2f(2-1)+2

We move all terms to the left:

f(2)-(2f(2-1)+2)=0

We add all the numbers together, and all the variables

f2-(2f1+2)=0

We add all the numbers together, and all the variables

f^2-(2f1+2)=0

We get rid of parentheses

f^2-2f1-2=0

We add all the numbers together, and all the variables

f^2-2f-2=0

a = 1; b = -2; c = -2;
Δ = b2-4ac
Δ = -22-4·1·(-2)
Δ = 12
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{12}=\sqrt{4*3}=\sqrt{4}*\sqrt{3}=2\sqrt{3}$
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{3}}{2*1}=\frac{2-2\sqrt{3}}{2}
$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{3}}{2*1}=\frac{2+2\sqrt{3}}{2}
$