Quadratic equation solve x2+2x-8=0

${\displaystyle \alpha }$ is a root of the equation ${\displaystyle p{x}^2+2qx+r=0}$ or not where the following determinant is given 0

g is related to one of the parent functions described in Section 1.6. Describe the sequence of transformations from f to g. ${\displaystyle g\left(x\right)=-\frac{1}{4}{(x+2)}^2-2}$

Solve the equation:
${\displaystyle \frac{{\left(9a^3{b}^4\right)}^{\frac{1}{2}}}{15a^{2}b}}$

Find the values of $k$ for which the simultaneous equations do not have a unique solution for $x,y$ and $z$.
Also show that when $k=-2$ the equations are inconsistent
$kx+2y+z=0$
$3x+0y-2z=4$
$3x-6ky-4z=14$
Using a determinant and setting to zero, then solving the quadratic gives
$\left|\begin{array}{ccc}k& 2& 1\\ 3& 0& -2\\ 3& -6k& -4\end{array}\right|=0$
$k=-2,k=\frac{1}{2}$
So far so good, but when subbing $-2$ for $k$
$-2x+2y+z=0...eqn1$
$3x+0y-2z=4...eqn2$
$3x+12y-4z=14...eqn3$
subbing eqn $2$ from eqn $3$ gives
$12y-2z=10$
$\Rightarrow y=\frac{5+z}{6}$
Subbing for $y$ into eqn $1$
$-2x+\frac{5+z}{3}-z=0$
$\Rightarrow x=\frac{5-2z}{6}$
Subbing for $y$ and $x$ into eqn $3$
$\frac{5-2z}{2}+10-2z=14$
$\Rightarrow z=\frac{-1}{2},x=1andy=\frac{3}{4}$
These values for $x,y$ and $z$ seem to prove unique solutions for these equations, yet from the determinant and also the question in the text book should they not be inconsistent?

How do you solve
${\displaystyle 64x^2-144x+81=0}$?

1) Do equations with $3$ variables require at least $3$ equation for us to solve without any dependent variable?2) if two equations of such kind equate to zero for eg: $a-b+2c=0$ and $3a+b+c=0$. Then using the matrice ,there is a method to solve them...explain that method.is there a proof or is it related to Gaussian method which is out of my scope?