Question 301655
Let N and N+2 be your consecutive even numbers. 
N is the smaller one.
{{{3N^2+(N+2)^2=84}}}
{{{3N^2+(N^2+4N+4)=84}}}
{{{4N^2+4N-80=0}}}
{{{N^2+N-20=0}}}
{{{(N+5)(N-4)=0}}}
Two solutions:
{{{N+5=0}}}
{{{N=-5}}}

Although it solves the equation, it's not even. 
So it it not a solution.
.
.
{{{N-4=0}}}
{{{N=4}}}
THe two numbers are 4 and 6.