6k^2-3k=2

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

6k^2-3k=2

We move all terms to the left:

6k^2-3k-(2)=0

a = 6; b = -3; c = -2;
Δ = b2-4ac
Δ = -32-4·6·(-2)
Δ = 57
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-\sqrt{57}}{2*6}=\frac{3-\sqrt{57}}{12}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{57}}{2*6}=\frac{3+\sqrt{57}}{12}
$