Is there a formal name for an equation that has no solution? I was wondering if there is a formal name for the equations which don't have any solution? 

For example consider this equation in $m$ :

$$ -2(3-m)+15=6m-4(m-20)$$

If we do the algebra we will get $2m-6m+4m=80-15+6 \Rightarrow 
0=71$ which implies no solution of $m$.
It seems that unsolvable, insolvable and insoluble are all used in this sense.  Personally I'd prefer either of the first two, to avoid confusion with the alternative meaning of insoluble in physics and chemistry.
The term that the textbook that we use for Algebra 1 is "contradiction" and the term used for an equation that has infinite solutions (4x + 2 =4x + 2) is called "identity"