Question

sec^2(x)=2x

Answer 1

I assume you are solving.
You will have to use some kind of iterative method such as Newton's Method

let y = sec^2(x) - 2x
dy/dx = 2(secx)(secx tanx) - 2
= 2 sec^2 x tanx - 2

Newton:
newx = x - (sec^2 x - 2x)/(2 sec^2 x tanx - 2)

pick any x
find newx
if newx is different from x, replace x with newx and repeat
If newx is equal to x up to some predetermined number of decimals, then
newx is your answer.
set your calculator to RADIANS and start with x = 2
after looking at a Wolfram graph
https://www.wolframalpha.com/input/?i=plot+y+%3D+sec%5E2%28x%29+%2C+y+%3D2x


x -------- newx
2 2.065152
2.065152 2.0820236
2.0820236 2.082834375
2.082834375 2.08283609
2.082283609 <b>2.08283609</b> , wow, correct to 8 decimals

Of course knowing that the trig function has a range of +infinite values, there will be an infinite number of solutions , e.g. x = 4.3672.. is another.