6k^2-3k-12=0

Solution for 6k^2-3k-12=0 equation:

6k^2-3k-12=0

a = 6; b = -3; c = -12;
Δ = b2-4ac
Δ = -32-4·6·(-12)
Δ = 297
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{297}=\sqrt{9*33}=\sqrt{9}*\sqrt{33}=3\sqrt{33}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3\sqrt{33}}{2*6}=\frac{3-3\sqrt{33}}{12}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3\sqrt{33}}{2*6}=\frac{3+3\sqrt{33}}{12}
$