Solve the following equation for x, giving your answer correct to 3 decimal places :

3x² - 12x - 1 = 0

Comparing 3x² - 12x - 1 = 0 with ax² + bx + c = 0 we get,

a = 3, b = -12 and c = -1.

We know that,

x = $\dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

Substituting values of a, b and c in above equation we get,

$\Rightarrow x = \dfrac{-(-12) \pm \sqrt{(-12)^2 - 4.(3).(-1)}}{2(3)} \\[1em] = \dfrac{12 \pm \sqrt{144 + 12}}{6} \\[1em] = \dfrac{12 \pm \sqrt{156}}{6} \\[1em] = \dfrac{12 \pm 12.49}{6} \\[1em] = \dfrac{12 + 12.49}{6} \text{ or } \dfrac{12 - 12.49}{6} \\[1em] = \dfrac{24.49}{6} \text{ or } \dfrac{-0.49}{6} \\[1em] = 4.082 \text{ or } -0.082$

Hence, x = 4.082 or -0.082