You can put this solution on YOUR website! Cos2x = cos(x + x) = cosx*cosx -sinx*sinx = cos^2(x) - sin^2(x)
We have the following identity: cos^2(x) + sin^2(x) = 1 ; sin^2(x) = 1 - cos^2(x)
2cos^2(x) - 1 = 5/7
cos^2(x) = 6/7
cos(x) = sqrt(6/7)
x = cos^(-1) (6/7)
at this point you put it into your calculator.
x ~ 22.5 degrees, or ~ pi/8.