In a nuclear fusion experiment, the magnetic flux boundary in a specific cross-section of the tokamak is modeled by the implicit equation
2x2y−3y2+x3=12 2x^2y - 3y^2 + x^3 = 12 2x2y−3y2+x3=12where x x\,x and y y\,y are spatial coordinates in decimeters.
Determine the equation of the tangent line to this boundary at the point P(2,2)P(2, 2)P(2,2), expressing your result in the form ax+by+c=0ax + by + c = 0ax+by+c=0, where a,ba, ba,b, and c c\,c are integers.
