Answer
{$\frac{1-\sqrt {85}}{6},\frac{1+\sqrt {85}}{6}$}
Work Step by Step
Step 1: We write $7=3x^{2}-x$ as $3x^{2}-x-7=0$.
Comparing $3x^{2}-x-7=0$ to the standard form of a quadratic equation, $ax^{2}+bx+c=0$, we find:
$a=3$, $b=-1$ and $c=-7$
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:
$x=\frac{-(-1) \pm \sqrt {(-1)^{2}-4(3)(-7)}}{2(3)}$
Step 4: $x=\frac{1 \pm \sqrt {1+84}}{6}$
Step 5: $x=\frac{1 \pm \sqrt {85}}{6}$
Step 6: $x=\frac{1-\sqrt {85}}{6}$ or $x=\frac{1+\sqrt {85}}{6}$
Step 7: Therefore, the solution set is {$\frac{1-\sqrt {85}}{6},\frac{1+\sqrt {85}}{6}$}.
