Solve the quadratic equation $\;$ $3x^2 - 12 x - 1 = 0$, $\;$ giving the answer to three significant figures.
Given quadratic equation: $\;$ $3x^2 - 12 x - 1 = 0$
Comparing with the standard equation $\;$ $ax^2 + bx + c = 0$ gives
$a = 3$, $\;$ $b = -12$, $\;$ $c = -1$
By quadratic formula, $\;$ $x = \dfrac{- b \pm \sqrt{b^2 - 4a c}}{2 a}$
$\begin{aligned}
i.e. \; \; x & = \dfrac{12 \pm \sqrt{\left(-12\right)^2 - 4 \times 3 \times \left(-1\right)}}{2 \times 3} \\\\
& = \dfrac{12 \pm \sqrt{156}}{6} \\\\
& = \dfrac{12 \pm 12.4899}{6} \\\\
& = \dfrac{24.4899}{6} \; \; or \; \; -\dfrac{0.4899}{6} \\\\
& = 4.0817 \;\; or \; \; -0.08165
\end{aligned}$
i.e. $\;$ $x = 4.08$ $\;$ or $\;$ $x = -0.0817$ $\;$ [correct to 3 significant figures]