Question 759579
The righthand number is inconvenient.  Just assign it to a variable and then work with it that way through most of the solution.  You cannot reduce 155*78/77^2.  


Let k=155*78/77^2


{{{x^2-5x+6=k}}}
{{{x^2-5x+(6-k)=0}}}

{{{x=(5-sqrt(4(6-k)))/2}}}  or {{{x=(5+sqrt(4(6-k)))/2}}}


Maybe work with the square root before simplifying, or this may be most of the needed simplifying.
{{{sqrt(24-4k)=2*sqrt(6-k)=2*sqrt((6-155*78/77^2))=2*sqrt((6*77^2-155*78)/77^2)
=(2/77)*sqrt(6*77^2-155*78)=(2/77)*sqrt(23484)=4*sqrt(5871)}}}, and that might or might not be more simplifiable....  3*1957 ?

{{{3*1957=3*19*103}}}, so not much more can be done with the square root.