Please enclose those fractions inside parentheses:
(3/4)x + 4 = (5/9) so that it's clear whether you meant 3x/4 or 3/(4x).
Identify the LCD. It is 36.
Mult. all 3 terms by this LCD:
36(3x/4) + 36(4) = 36(5/9)
Reduce: 27x + 144 = 20
Subtract 144 from both sides: 27x = 20 - 144 = -124
Solve for x: x = -124/27 = -4.59 (rounded off to the nearest hundredth)