As is you cannot solve for k.
To find k you'd need to know how many real roots the equation has and then use the discriminant as appropriate.
Alternatively you can find x in terms of k using your favourite method
this one is not so bad.
if we use the idea of comparing coefficients as has been shown you can think like this.
now you have all positive terms. the coefficients are 4 and 6. which factor to and . so you have 2 factors of each coeffient just like the general form. now just substitute all the inormation into the general factors.
now that you know k solve your linear equations to find the roots.
here is a extra think...
to check k I do this.
2 real roots.
now if we do like before we get this.
now we check with k and decimals.
the inequalities is only telling you what value k is greater then or less then not k itself.
I think you guys over think on this one.
for quadratic equations this is true. all partial products of factors.
and we have the rule in this case a and c only have 2 factors each so they fall nicely into the LHS but you could use the same method for any ac coefficients that factor.