$x^{2} + \frac{x - 1}{3} = 0$

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Solution

Given: $x^{2} + \frac{x - 1}{3} = 0$
On rewriting this equation in the standard form of the quadratic equation, we get:

3x² + x – 1 = 0
On comparing this equation with ax² + bx + c = 0, we get:

a = 3, b = 1 and c = –1
For the quadratic equation ax² + bx + c = 0, we know that the quadratic formula is
$x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$
On substituting a = 3, b = 1 and c = –1, we get:
$x = \frac{- 1 \pm \sqrt{1^{2} - 4 \times 3 \times (- 1)}}{2 \times 3} = \frac{- 1 \pm \sqrt{1 + 12}}{6} = \frac{- 1 \pm \sqrt{13}}{6}$
Thus, the solution of the given quadratic equation is x = $\frac{- 1 + \sqrt{13}}{6}, \frac{- 1 - \sqrt{13}}{6}$ .

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