Solve for x
x=\frac{2^{\frac{2}{3}}\left(\sqrt[3]{\sqrt{113}-9}-\sqrt[3]{\sqrt{113}+9}\right)}{6}\approx -0.402319938
x=0
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3t^{2}+2t+1=0
Substitute t for x^{2}.
t=\frac{-2±\sqrt{2^{2}-4\times 3\times 1}}{2\times 3}
All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Substitute 3 for a, 2 for b, and 1 for c in the quadratic formula.
t=\frac{-2±\sqrt{-8}}{6}
Do the calculations.
t\in \emptyset
Since the square root of a negative number is not defined in the real field, there are no solutions.
x\in \emptyset
Since t=x^{2}, the original equation does not have any solutions.
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