12k^2=2-5k

Solution for 12k^2=2-5k equation:

12k^2=2-5k

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

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