Question 1208922
.
<pre>

Write this equation in the standard quadratic form

    6k^2 + k - 2 = 0.


To find k, apply the quadratic formula

    {{{k[1,2]}}} = {{{(-1 +- sqrt((-1)^2 - 4*6*(-2)))/(2*6)}}} = {{{(-1 +- sqrt(49))/12}}} = {{{(-1 +- 7)/12}}}.


They want k  be positive - so take this unique positive root  k = {{{(-1+7)/12}}} = {{{6/12}}} = {{{1/2}}}.


At this point, the solution is complete.


<U>ANSWER</U>.  k = {{{1/2}}}.
</pre>

Solved.


------------------------


On solving quadratic equations using the quadratic formula, &nbsp;see the lessons 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/Introduction-Into-Quadratics.lesson>Introduction into Quadratic Equations</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/proof-of-quadratic-by-completing-the-square.lesson>PROOF of quadratic formula by completing the square</A>

in this site.



If factoring requires mental efforts from you more than 5 - 7 - 10 seconds 
and is not requested in the assignment, use the quadratic formula.


It is the general rule to save your mind from unnecessary exercises for real work.