12k2-5k=2

Solution for 12k2-5k=2 equation:

12k^2-5k=2

We move all terms to the left:

12k^2-5k-(2)=0

a = 12; b = -5; c = -2;
Δ = b2-4ac
Δ = -52-4·12·(-2)
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-11}{2*12}=\frac{-6}{24}
=-1/4
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+11}{2*12}=\frac{16}{24}
=2/3
$