First we square both sides:
#(sqrt(4)/sqrt(4x+9))^2=(sqrt(8x+2))^2#
#(sqrt(4))^2/(sqrt(4x+9))^2=(sqrt(8x+2))^2#
#4/(4x+9)=8x+2#
Now we can rearrange and make it eqial to 0:
#4=(8x+2)(4x+9)#
#(8x+2)(4x+9)-4=0#
Now expand brackets:
#(8x*4x)+(2*4x)+(8x*9)+(2*9)-4=0#
#32x^2+8x+72x+18-4=0#
#32x^2+80x+14=0#
We can remove out common factors:
#32x^2+80x+14=0#
#16x^2+40x+7=0#
#x=(-b+-sqrt(b^2-4ac))/(2a)#
#x=(-40+-sqrt(40^2-4(16*7)))/32#
#=(-40+-sqrt(1600-4(112)))/32#
#=(-40+-sqrt(1600-448))/32#
#=(-40+-sqrt(1152))/32#
#=(-40+sqrt(1152))/32or(-40-sqrt(1152))/32#
#~~-2.31or-0.19#
