Solve the following system with non-linear functions graphically.
\[
\begin{array}{l}
y=2 x^{\frac{6}{5}} \\
y=6 x^{\frac{3}{5}}-4
\end{array}
\]
Enter the $\mathrm{x}$-value(s) of the solution(s) below and round your answer(s) to three decimal places.
There are four solutions and they are: $x= \pm$ or $x= \pm$
There are two solutions and they are: $x_{1}=$ or $x_{2}=$
There is one solution and it is: $x_{1}=$
There is no solution.

Step 1 ：Setting the two expressions for $y$ equal to each other, it follows that $2x^{\frac{6}{5}} = 6x^{\frac{3}{5}} - 4$.

Step 2 ：Re-arranging, $2x^{\frac{6}{5}} - 6x^{\frac{3}{5}} + 4 = 0$.

Step 3 ：Let $t = x^{\frac{3}{5}}$, then the equation becomes $2t^2 - 6t + 4 = 0$.

Step 4 ：For there to be exactly one solution for $t$, then the discriminant of the given quadratic must be equal to zero.

Step 5 ：Thus, $(-6)^2 - 4 \cdot 2 \cdot 4 = 36 - 32 = 4$.

Step 6 ：Since the discriminant is not equal to zero, there is no $t$ that satisfies the equation, which means there is no $x$ that satisfies the original system of equations.

Step 7 ：So, there is \(\boxed{\text{no solution}}\).