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Java 7, 130 bytes

Golfed:

double[]w(int s,int f){double n=s+f,z=1.96,x=z*z,p=s+x/2,d=z*Math.sqrt(s*f/n+x/4),m=1/(n+x);return new double[]{m*(p-d),m*(p+d)};} 

Ungolfed:

double[] w(int s, int f) { double n = s + f, z = 1.96, x = z * z, p = s + x / 2, d = z * Math.sqrt(s * f / n + x / 4), m = 1 / (n + x); return new double[] { m * (p - d), m * (p + d) }; } 

[Try it online][1]Try it online

Returns an array of type double of length 2, can probably be golfed more. [1]: https://ideone.com/CHeljM

Java 7, 130 bytes

Golfed:

double[]w(int s,int f){double n=s+f,z=1.96,x=z*z,p=s+x/2,d=z*Math.sqrt(s*f/n+x/4),m=1/(n+x);return new double[]{m*(p-d),m*(p+d)};} 

Ungolfed:

double[] w(int s, int f) { double n = s + f, z = 1.96, x = z * z, p = s + x / 2, d = z * Math.sqrt(s * f / n + x / 4), m = 1 / (n + x); return new double[] { m * (p - d), m * (p + d) }; } 

[Try it online][1]

Returns an array of type double of length 2, can probably be golfed more. [1]: https://ideone.com/CHeljM

Java 7, 130 bytes

Golfed:

double[]w(int s,int f){double n=s+f,z=1.96,x=z*z,p=s+x/2,d=z*Math.sqrt(s*f/n+x/4),m=1/(n+x);return new double[]{m*(p-d),m*(p+d)};} 

Ungolfed:

double[] w(int s, int f) { double n = s + f, z = 1.96, x = z * z, p = s + x / 2, d = z * Math.sqrt(s * f / n + x / 4), m = 1 / (n + x); return new double[] { m * (p - d), m * (p + d) }; } 

Try it online

Returns an array of type double of length 2, can probably be golfed more.

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Java 7, 130 bytes

Golfed:

double[]w(int s,int f){double n=s+f,z=1.96,x=z*z,p=s+x/2,d=z*Math.sqrt(s*f/n+x/4),m=1/(n+x);return new double[]{m*(p-d),m*(p+d)};} 

Ungolfed:

double[] w(int s, int f) { double n = s + f, z = 1.96, x = z * z, p = s + x / 2, d = z * Math.sqrt(s * f / n + x / 4), m = 1 / (n + x); return new double[] { m * (p - d), m * (p + d) }; } 

[Try it online][1]

Returns an array of type double of length 2, can probably be golfed more. [1]: https://ideone.com/CHeljM