Quadratic Equation - Trick Question

This is a polynomial equation that has rational (fraction) exponents. It is an equation that will generally be solved by U-substitution, but more importantly, the observation that the lead exponent is twice as large as the middle exponent. It is the type of question that is often given for extra credit or as a critical thinking question.

[douglasmullen]

I made the mistake of adding X2/5th + X1/5th-6=0, which left, X 3/5th-6=0, I then added +6 to both sides leaving X 3/5th=6, I then unversed the 3/5 to 5/3, 3/5 it looked like this [X3/5] 5/3 =6 5/3th, the inverse cancelled out the 3/5 on the left side looking like this X=6 5/3. I then divide the 3 into the 6 leaving 2x5=10, X=10 which was wrong, thank you for showing me the step by step method to solving this question.