Greetings Milena!

The first thing you should do is to solve for sinx:

sinx = sqrt(2)/2

Now, to solve x, I am sorry to have to tell you that without a calculator, the only real way to solve this is by knowing the unit circle and its values. In this case x would have to equal 45 degrees, or 135 degrees provided your answer needs to be between 0 and 360 degrees.

Since most teachers want answers like this in radians, use the conversion factor pi radians = 180 degrees to convert.

You can use either knowledge of a Unit circle and it's values, or a calculator to solve the final calculation.

First, solve for sin(x) by dividing 2 from both sides:           sin(x) = sqrt(2)/2

Then, take the inverse sin to solve for x by itself:           x = sin^-1[sqrt(2)/2]

This value can be computed via calculator or unit circle knowledge, to be 45 or 135 degrees, since you must find all values between 0 and 360 degrees.

Here's a link to a site where you can play around with unit circles to get a better idea as to how they work:
http://www.mathsisfun.com/geometry/unit-circle.html

2sinx=Square root of 2

x = arcsin ((2)^1/2/2) = arcsin 1/(2^1/2)

From the unit circle arcsin 1/(2^1/2) = ∏/4 and 3∏/4.  All values would be (∏/4 + 2n∏) and (3∏/4 + 2n∏) where n = any integer.