Question 210762
OK.. first step is not to panic :-)
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Next step is remember some laws about exponents. Namely that:
{{{x^(2/3)=(x^2)^(1/3)}}}
You can apply that to the left side of the equation:
{{{(6x-5)^(2/3) = x^(1/3)}}}
{{{((6x-5)^2)^(1/3)=x^(1/3)}}}
Now square that binomial:
{{{(36x^2-60x+25)^(1/3)=x^(1/3)}}}
Cube both sides of the equation:
{{{36x^2-60x+25=x}}}
Equate to zero:
{{{36x^2-61x+25=0}}}
This is looking much more manageable now. just apply the quadratic formula to this and you are done:
*[invoke quadratic "x", 36, -61, 25 ]


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Good Luck,
tutor_paul@yahoo.com