7 + 6 ln x - 22.6 = 0

7 + 6 ln x - 22.6 = 0     simplify

6 ln x - 15.6  =  0          add 15.6 to both sides

6 ln x = 15.6     divide both sides by 6

ln x = 15.6 / 6

So

x =  e^(15.6 / 6)  = about 13.46