Question

x lnx - 30 + 5 lnx - 6x = 0

Answer 1

Are you supposed to solve for x?

(5+x)ln x - 6x = 30

That looks to me like a transcendental equation that will have to be solved by iteration or graphing.
Try different values of x on the left side until you get +30.
If x = 0.01, (5+x)ln x - 6x = -23.12
If x = 0.05, (5+x)ln x - 6x = -15.4
If x = 0.1, (5+x)ln x - 6x = -12.3
If x = 1, (5+x)ln x - 6x = -6.0
If x = 2, (5+x)ln x - 6x = -7.15
If x = 10, (5+x)ln x - 6x = -25.6
If x = 20, (5+x)ln x - 6x = -45.1
It looks like there is no value of x for which the equation is valid.