So I have the formula and values substituted in correctly - but now the simple algebra part is killing me.
x = vt + 1/2at^2
.06=(2*10^3)t + 1/2(4*10^7)t^2
What is t?
$\displaystyle .06 = (2*10^3)t + 1/2(4*10^7)t^2$
$\displaystyle .06 = 2000t + 20000000t^2$
Set equal to 0 and rearrange:
$\displaystyle 20000000t^2 + 2000t - 0.06 = 0$
Use the quadratic formula:
$\displaystyle \begin{aligned}
t &= \dfrac{-2000 \pm \sqrt{2000^2 - 4(20000000)(-0.06)}}{2(20000000)} \\
&= \dfrac{-2000 \pm \sqrt{4000000 + 4800000}}{40000000} \\
&= \dfrac{-2000 \pm \sqrt{8800000}}{40000000} \\
&\approx 2.42 \times 10^{-5}, -1.24 \times 10^{-4}
\end{aligned}$