12k-12k^2=2

Solution for 12k-12k^2=2 equation:

12k-12k^2=2

We move all terms to the left:

12k-12k^2-(2)=0

a = -12; b = 12; c = -2;
Δ = b2-4ac
Δ = 122-4·(-12)·(-2)
Δ = 48
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:

$\sqrt{\Delta}=\sqrt{48}=\sqrt{16*3}=\sqrt{16}*\sqrt{3}=4\sqrt{3}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{3}}{2*-12}=\frac{-12-4\sqrt{3}}{-24}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{3}}{2*-12}=\frac{-12+4\sqrt{3}}{-24}
$