Question 731924
You might have meant {{{3x^2 + 2x = 77}}}
You could multiply both sides of the equal sign times {{{highlight(3)}}} to get
{{{9x^2+6x=231}}}
From there
{{{9x^2+6x=231}}} --> {{{9x^2+6x+1=231+1}}} --> {{{(3x+1)^2=232}}}
So,
either {{{3x+1=sqrt(232)}}} --> {{{3x=-1+sqrt(235)}}} ,
or {{{3x+1=-sqrt(232)}}} --> {{{3x=-1-sqrt(232)}}}
You can write both answers as
{{{3x=-1 +- sqrt(232)}}} --> {{{highlight(x=(-1 +- sqrt(232))/3)}}}
 
NOTE: because {{{232=4*58}}} --> sqrt(252)=sqrt(4*58)=sqrt(4)*sqrt(58)=2sqrt(58)}}}
so {{{highlight(x=(-1 +- 2sqrt(58))/3)}}} is another way to express the anmswer.