I have a nonlinear system of 3 equations with 27 constants and 3 unknowns x, y, z
K1 = x*(uX1*x^2+vX1*x+wX1) + y*(uX2*y^2+vX2*y+wX2) + z*(uX3*z^2+vX3*z+wX3)
K2 = x*(uY1*x^2+vY1*x+wY1) + y*(uY2*y^2+vY2*y+wY2) + z*(uY3*z^2+vY3*z+wY3)
K3 = x*(uZ1*x^2+vZ1*x+wZ1) + y*(uZ2*y^2+vZ2*y+wZ2) + z*(uZ3*z^2+vZ3*z+wZ3)
The equations are polynoms of degree 3 and only real and positive solutions for x, y, z are of interest for me.
Is there any method/algorithm that resolves either this system fastly (for real-time applications), either finds exact solutions?