Swap the 2nd and 3rd terms on the left to get the terms together
for each letter:

 

Subtract the constant term from both sides:





Factor out 16 out of the first two terms, and 1 out of
the last two terms:



We complete the square inside the first parentheses:
1. Multiply the coefficient of x, which is 4, by one-half, getting 2.
2. Square 2, getting 4.
3. Add +4 at the end of the first parentheses.
4. Since the number in front of the parentheses is 16, adding 4 inside
   the parentheses amounts to adding 16∙4 or 64 to the left side, so
   we add 64 to the right side:



We complete the square inside the second parentheses:
1. Multiply the coefficient of y, which is -2, by one-half, getting -1.
2. Square -1, getting +1.
3. Add +1 at the end of the first parentheses.
4. Since the number in front of the parentheses is 1, adding 4 inside
   the parentheses amounts to adding 1∙1 or 1 to the left side, so
   we add 1 to the right side:



Next we factor the quadratics in the parentheses:





This does not represent a conic because the left side is positive
and the right side is negative.  

We get 1 on the right side by dividing each term by -2





We divide top and bottom of the first fraction by 16







If this were a real conic, there would not be a negative number
on the bottom of either term, but only positive numbers.

Did you copy the problem wrong?

Edwin

Edwin just derived this standard conic equation for you


     +  = -1.


This equation describes the empty set of points.


Indeed, the equation has the left side non-negative (as the sum of two squares), while its right side is the negative number,

so the equation has no real solutions.