We want resolve  21*x^4 + 73*x^3 - 57*x^2 + 73*x - 78 = 0  by using equp.htm. We prove with a = -10 and b = 10, and click "test".

For x → ∞ and for x → −∞ a polynomial function of degree 4 tends to ∞.  F(−6) = 8880; F(0) = −78; F(2) = 760.  I have to look for a solution between −6 and 0, for another between 0 and 2.

We can draw the graphs with JavaScript; for example by this script:

But the outputs printed by the program (obtained by clicking "test") allow you not to draw the graph.  Between −6 and 0:

until I get:

Similarly, between 0 and 2:

The solutions are −(4+1/3) and 0.857142857142857142... = 6/7 (I can use this program to find the fraction equal to 0.857142857142857...: M=857142, N=99999, ... -> 6/7).
 

We can draw the graphs also with the script x4321  (see the code;  se also here).

I can also use R. I would get:

or with PHP (see "a zoom" here):

or with Desmos: