I assume this is meant to be x = 1/(3x) + 5
If so, multiply all terms by 3x, to get. 3x2 = 1 + 15x
Subtract 1 + 15x from both sides: 3x2 - 15x - 1 = 0
This is a quadratic equation so the two solutions are given by:
x1 = (15 + sqrt(152 - 4*3*(-1)))/(2*3) → (15 + sqrt(237))/6
x2 = (15 - sqrt(152 - 4*3*(-1)))/(2*3) → (15 - sqrt(237))/6
If the original equation is meant to be x = 1/(3x + 5) then multiply through by 3x + 5 to get
3x2 + 5x = 1. Subtract 1 from both sides:
3x2 + 5x -1 = 0
The solutions are:
x1 = (-5 + sqrt(25 + 12))/6 → (-5 + sqrt(37))/6
x2 = (-5 sqrt(37))/6