#1/(2x+3)+1/(4x-3)=5#
Take LCM of denominators #(2x+3)(4x-3)#
Multiply both sides by #(2x+3)(4x-3)#
#(2x+3)(4x-3)(1/(2x+3)+1/(4x-3))=5(2x+3)(4x-3)#
#((2x+3)(4x-3))/(2x+3)+((2x+3)(4x-3))/(4x-3)=5(2x+3)(4x-3)#
Cancel Equal like terms
#(4x-3)+(2x+3)=5(2x+3)(4x-3)#
#6x=5(8x^2-6x+12x-9)#
#6x=5(8x^2+6x-9)#
#6x=40x^2+30x-45#
Subtract #6x# from both side
#6x-6x=40x^2+30x-45-6x#
#0=40x^2+24x-45#
#40x^2+24x-45=0#
comparing with #ax^2+bx+c=0#
#a=40, b=24, c=-45#
Solution #x=(-b+-sqrt(b^2-4ac))/(2a) #
#x=(-24+-sqrt((24)^2-4(40)(-45)))/(2(40))#
#x=(-24+-sqrt(576+7200))/80#
#x=(-24+-sqrt(7776))/80#
#x=(-24+-sqrt(1296xx6))/80#
#x=(-24+-36sqrt(6))/80#
#x=(-3+-3sqrt(6))/10#
