f(2)=-4f(2-1)+2

Solution for f(2)=-4f(2-1)+2 equation:

f(2)=-4f(2-1)+2

We move all terms to the left:

f(2)-(-4f(2-1)+2)=0

We add all the numbers together, and all the variables

f2-(-4f1+2)=0

We add all the numbers together, and all the variables

f^2-(-4f1+2)=0

We get rid of parentheses

f^2+4f1-2=0

We add all the numbers together, and all the variables

f^2+4f-2=0

a = 1; b = 4; c = -2;
Δ = b2-4ac
Δ = 42-4·1·(-2)
Δ = 24
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:

$\sqrt{\Delta}=\sqrt{24}=\sqrt{4*6}=\sqrt{4}*\sqrt{6}=2\sqrt{6}$
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{6}}{2*1}=\frac{-4-2\sqrt{6}}{2}
$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{6}}{2*1}=\frac{-4+2\sqrt{6}}{2}
$