Question 29636
I am reading this problem as ....
{{{ (3d-7)/(2d) = (3d-2)/(3d^2) }}}
cross multiply
{{{ (3d^2)(3d-7) = (2d)(3d-2) }}}
distribute
{{{ 9d^3 - 21d^2 = 6d^2 - 4d }}}
move everything to the left
{{{ 9d^3 - 21d^2 - 6d^2 + 4d = 0 }}}
combine like terms
{{{ 9d^3 - 27d^2 + 4d = 0 }}}
since the power is cubed, there will be 3 solutions.
for the first, factor out a d
{{{ d(9d^2 - 27d + 4) = 0 }}}
the first solution is d=0
the trinomial can not be factored.  Use the quadratic formula to solve.
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
a = 9     
b = -27    
c = 4
substitute these numbers into the equation
{{{x = (-(-27) +- sqrt( (-27)^2-4*9*4 ))/(2*9) }}}
simplify
{{{x = (27) +- sqrt( ( 729-144 ))/(18) }}}
simplify again
{{{x = (27) +- sqrt( ( 585 ))/(18) }}}
root out 585
585 = 3*3*5*13
{{{ sqrt( 585) = 3*sqrt(65) }}}
the + and - make for the 2 other solutions.
{{{x = (27 +- 3*sqrt(65))/(18) }}}
reduce all cofficients by dividing each by 3
{{{x = (9 +- 1*sqrt(65))/(6) }}}

Those are your 3 answers