(5x + 35)^1/2 = 8 +x

First, square both sides to elimate the square root-

Your equation becomes: X2 +16X +64 = 5X + 35
Group everything: X2 +11X +29 = 0

Find delta, the discrimant: Delta = 5

X1 = (-11 -Sqrt(5) )/2
X2 = (-11 +SQRT(5) )/2