other Quadratic equations

The problem is 7x^3-x+1=x^3+3x^2+x. Find all real answers. I came upwith two answers 3x^2=1 and 2x=1/2. The first answer just does not look right. I must be forgeting something!

You can check them by putting in x=1/4 (the second answer), and then x=+- sqrt(1/3) These are three answers that need to be checked.

If the equation balances, the answers are correct.

The other way of checking it is to graph
y=7x^3-x+1-x^3-3x^2-x. yes, combine the terms. Where y is zero, ie, crossing the x axis, that is a real solution.

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