f(2)=65538

Solution for f(2)=65538 equation:

f(2)=65538

We move all terms to the left:

f(2)-(65538)=0

We add all the numbers together, and all the variables

f^2-65538=0

a = 1; b = 0; c = -65538;
Δ = b2-4ac
Δ = 02-4·1·(-65538)
Δ = 262152
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:

$\sqrt{\Delta}=\sqrt{262152}=\sqrt{36*7282}=\sqrt{36}*\sqrt{7282}=6\sqrt{7282}$
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{7282}}{2*1}=\frac{0-6\sqrt{7282}}{2}
=-\frac{6\sqrt{7282}}{2}
=-3\sqrt{7282}
$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{7282}}{2*1}=\frac{0+6\sqrt{7282}}{2}
=\frac{6\sqrt{7282}}{2}
=3\sqrt{7282}
$