f(2)=1-f2

Solution for f(2)=1-f2 equation:

f(2)=1-f2

We move all terms to the left:

f(2)-(1-f2)=0

We add all the numbers together, and all the variables

-(-1f^2+1)+f2=0

We add all the numbers together, and all the variables

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

We get rid of parentheses

f^2+1f^2-1=0

We add all the numbers together, and all the variables

2f^2-1=0

a = 2; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·2·(-1)
Δ = 8
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:

$\sqrt{\Delta}=\sqrt{8}=\sqrt{4*2}=\sqrt{4}*\sqrt{2}=2\sqrt{2}$
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{2}}{2*2}=\frac{0-2\sqrt{2}}{4}
=-\frac{2\sqrt{2}}{4}
=-\frac{\sqrt{2}}{2}
$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{2}}{2*2}=\frac{0+2\sqrt{2}}{4}
=\frac{2\sqrt{2}}{4}
=\frac{\sqrt{2}}{2}
$