$\textbf{Answer:}$

$x=0 \ and \ x= \frac{1}{24}$

$\textbf{Explaination:}$

$Method \ 1:$

For the method we will use the quadratic formula

$x = \frac{-b \pm \sqrt{b^2-4ac}}{2a}$ where $ a=-12 , b= 0.5 \ and \ c=0$

$x= \frac{-0.5 \pm \sqrt{(-0.5)^2-4(-12)(0)}}{2(-12)}$

$ \implies x = \frac{-0.5 + \sqrt{(0.5)^2-4(-12)(0)}}{2(-12)} \ and \ x = \frac{-0.5 - \sqrt{(0.5)^2-4(-12)(0)}}{2(-12)}$

$\implies x = 0 \ and \ x = \frac{1}{24}$

$Method \ 2:$

$0.5x-12x^2=0$

$12x^2-0.5x=0$ (starting with the term with the highest degree and multiplying through by -1)

$x(12x-0.5) = 0$ (factoring out x)

$ \implies x= 0 \ and \ 12x-0.5 =0$

$\implies x=0 \ and \ x= \frac{0.5}{12} = \frac{1}{24}$