2.2 .3 \quad 3 x^{\frac{2}{3}}-7 x^{\frac{1}{5}}+2=0

To tackle the equation \(3 x^{\frac{2}{3}} - 7 x^{\frac{1}{5}} + 2 = 0\), you might find it helpful to use substitution. Let’s define \(y = x^{\frac{1}{15}}\). Then \(x^{\frac{2}{3}} = y^{10}\) and \(x^{\frac{1}{5}} = y^3\). This transforms the equation into a polynomial form, making it easier to solve for \(y\). Once you obtain the values of \(y\), it's a fun process of reverting back to find the original variable \(x\) via \(x = y^{15}\). Keep an eye out for extraneous roots introduced during the substitution, as they can lead to confusion when validating your solutions.