Answer
{$\frac{-1 - i\sqrt {59}}{6},\frac{-1 + i\sqrt {59}}{6}$}
Work Step by Step
Step 1: Comparing $3x^{2}+x+5=0$ to the standard form of a quadratic equation, $ax^{2}+bx+c=0$, we find:
$a=3$, $b=1$ and $c=5$
Step 2: The quadratic formula is:
$x=\frac{-b \pm \sqrt {b^{2}-4ac}}{2a}$
Step 3: Substituting the values of a, b and c in the formula:
$x=\frac{-(1) \pm \sqrt {(1)^{2}-4(3)(5)}}{2(3)}$
Step 4: $x=\frac{-1 \pm \sqrt {1-60}}{6}$
Step 5: $x=\frac{-1 \pm \sqrt {-59}}{6}$
Step 6: $x=\frac{-1 \pm \sqrt {-1\times59}}{6}$
Step 7: $x=\frac{-1 \pm (\sqrt {-1}\times\sqrt {59})}{6}$
Step 8: $x=\frac{-1 \pm (i\times \sqrt {59})}{6}$
Step 9: $x=\frac{-1 \pm i\sqrt {59}}{6}$
Step 10: $x=\frac{-1 - i\sqrt {59}}{6}$ or $x=\frac{-1 + i\sqrt {59}}{6}$
Step 11: Therefore, the solution set is {$\frac{-1 - i\sqrt {59}}{6},\frac{-1 + i\sqrt {59}}{6}$}.
