Double the equation throughout to get rid of the decimal on the left: 1+6x=-5.8, then subtract 1 from each side of the equation: 6x=-6.8 (note that the right side becomes more negative). Divide both sides by 2 because both sides have an even number: 3x=-3.4. Finally divide both sides by 3: x=-1.1333. The decimal goes on for ever, but you just need to provide a few places.
Alternative solution: multiply the equation by 10 to get rid of all decimals: 5+30x=-29. Subtract 5 from both sides: 30x=-34. Divide both sides by 2: 15x=-17. Divide both sides by 15: x=-17/15.