I will guess that the exercise is contained in the subject line: "Determine tanx if secx=(sqrt14)/2 and is in the second quadrant".

I don't know what you're doing in your post...? Instead, try working from what you've learned about trig functions, the four quadrants, and the unit circle.

The secant is the reciprocal of the cosine, so cos(x) = 2/sqrt[14] = 2sqrt[14]/14 = sqrt[14]/7. You are given that the angle x is in the second quadrant, where cosine and tangent are negative, so I'll guess that sec(x) is actually supposed to be a negative value...?

Draw a right triangle in the second quadrant, with the non-right base angle being at the origin and the base being on the x-axis. The x-value (the "length" of the side on the x-axis) is obviously the negative value, so put -sqrt[14] here, on the "adjacent" side. Since cos(x) = -sqrt[14]/7, then the hypotenuse is clearly 7.

Use the Pythagorean Theorem to find the length of the side that parallels the y-axis. Then read off the (exact) value of the tangent from the triangle.