Answer
$\displaystyle \frac{-1+\sqrt{73}}{6}\approx 1.257$
$\displaystyle \frac{-1-\sqrt{73}}{6}\approx-1.591$
Work Step by Step
Set the $RHS$ to 0 by subtracting 6 from both sides
$3k^{2}+k=6\qquad.../-6$
$3k^{2}+k-6=0$
Use the quadratic formula:
(For $ax^{2}+bx+c=0,\ x=\displaystyle \frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$ )
$k=\displaystyle \frac{-1\pm\sqrt{1-4(3)(-6)}}{2(3)}=\frac{-1\pm\sqrt{1+72}}{6}$
$k=\displaystyle \frac{-1\pm\sqrt{73}}{6}$
Solutions:
$\displaystyle \frac{-1+\sqrt{73}}{6}\approx 1.257$ and
$\displaystyle \frac{-1-\sqrt{73}}{6}\approx-1.591$.
