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