I have to mention, that I know nothing about the STL format. But here is what I tried. First you have to get used to Mathematica formula conventions. Expecially "=" is used as assignment. You are looking for "==" which is equality. To plot your function I chose ContourPlot3D:

ContourPlot3D[(x^2 + 9/4 y^2 + z^2 - 1)^3 - x^2 z^3 - 9/(80) y^3 z^3 == 0, {x, -2, 2}, {y, -2, 2}, {z, -2, 2}]

Then I use Export to get the STL file:

Export["<insert path>\\heart.stl", %]

Replace the "\" with "/" if you are on a linux/unix system. I can't check the contents of the STL file - it might be neccessary to fine-tune the settings of ContourPlot3D to get the desired result. The "%" is an abbreviation for the last output.