Question 449026
{{{1/(3v-6) -4= -2/(v-2)}}}........common denominator


{{{(1 -4(3v-6))/(3v-6)= -2/(v-2)}}}


{{{(1 -12v+24)/(3v-6)= -2/(v-2)}}}


{{{(-12v+25)/(3v-6)= -2/(v-2)}}}......cross multiply


{{{(-12v+25)(v-2)= -2(3v-6)}}}


{{{-12v^2+24v+25v-50= -6v+12)}}}


{{{-50-12=12v^2-25v-24v -6v)}}}


{{{-62=12v^2-55v)}}}


{{{12v^2-55v+62=0)}}}.......use quadratic formula


{{{v = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 


{{{v = (-(-55) +- sqrt((-55)^2-4*12*62 ))/(2*12) }}} 


{{{v = (55 +- sqrt(3025-2976))/24 }}} 


{{{v = (55 +- sqrt(49))/24 }}} 


{{{v = (55 +- 7)/24 }}} 


{{{v = (55 + 7)/24 }}} 


{{{v = 62/24 }}} 


{{{v = 2.58}}}

or


{{{v1 = (55 - 7)/24 }}} 


{{{v1 = 48/24 }}} 


{{{v1 = 2}}}


so, your solutions are:{{{v = 2.58}}} or {{{v = 2}}}



let's see it on a graph:

{{{ graph( 500, 500, -5, 5, -10, 10, 12x^2-55x+62) }}}