Question

use the quadratic formula to solve for x.
$6x^2 - 3x - 1 = 0$
(if there is more than one solution, separate them with commas.)
$x = \square$

Explanation:

Step1: Identify a,b,c from equation

For $6x^2 - 3x - 1 = 0$, $a=6$, $b=-3$, $c=-1$

Step2: Recall quadratic formula

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

Step3: Compute discriminant

$b^2-4ac=(-3)^2-4(6)(-1)=9+24=33$

Step4: Substitute values into formula

$$x=\frac{-(-3)\pm\sqrt{33}}{2(6)}=\frac{3\pm\sqrt{33}}{12}$$

Answer:

$x=\frac{3+\sqrt{33}}{12}, \frac{3-\sqrt{33}}{12}$