I was studying equations, and came across the term Transcedental being use for equations of the form, $$ \sin(x) -e^{x} + x^{2 }= 0 $$ From what I understand, the equations involving terms like exp, sin are called transcedental. I also googled and found that equations of the form $\space a_{n}x^{n} + a_{n-1}x^{n-1} ... + a_{0} = 0 \space$ (the lhs is a polynomial) are called algebraic. Finally, then what are equations of the form $ \space x^{\frac{3}{2}} - 2x + x^{\frac{5}{3}} = 0 \space $ called?
NOTE: These are just random examples.
A transcendental equation is an equation that is not algebraic. The equation $x^{\frac{3}{2}} - 2x + x^{\frac{5}{3}} = 0$ is algebraic, since its solutions are solutions of some polynomial equation (which takes some manipulation to find).