Math sum and reciprocal help

Please help me solve this! Thanks!

The sum of a number and 6 times its reciprocal is 11/2. Find the numbers.

Thanks!

Let the number be n

Given, n+6*(1/n)= 11/2

n+6/n=11/2

(n*n+6)/n=11/2

(n^2+6)/n =11/2

Cross multiply:

2(n^2+6)=11n

2n^2+12=11n

2n^2-11n+12=0

2n^2-8n-3n+12=0

2n(n-4)-3(n-4)=0

(2n-3)(n-4) = 0

n=3/2 or n=4

.....

Let such a number be x.

The sum of a number and 6 times its reciprocal = 11/2.
=> x + 6/x = 11/2
=> 2x^2 + 12 = 11x, multiplying by 2x
=> 2x^2 - 11x + 12 = 0.
=> (2x-3)(x-4) = 0
=> x = 3/2 or x = 4.

You can check these values again.
3/2 + 6*2/3 = 9/6 + 24/6 = 33/6 = 11/2
4 + 6*1/4 = 11/2.

Therefore, there are two solutions.
x = 3/2 or x = 4