Question

solve for x. write both solutions, separated by a comma.
6x² - x - 12 = 0
enter the correct answer.

Explanation:

Step1: Identify quadratic coefficients

For $6x^2 - x - 12 = 0$, $a=6$, $b=-1$, $c=-12$

Step2: Apply quadratic formula

Quadratic formula: $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$
Substitute values:

$$ x = \frac{-(-1) \pm \sqrt{(-1)^2 - 4(6)(-12)}}{2(6)} $$

Step3: Calculate discriminant

Compute $\sqrt{1 + 288} = \sqrt{289} = 17$
Expression becomes: $x = \frac{1 \pm 17}{12}$

Step4: Solve for both roots

First root: $x = \frac{1 + 17}{12} = \frac{18}{12} = \frac{3}{2}$
Second root: $x = \frac{1 - 17}{12} = \frac{-16}{12} = -\frac{4}{3}$

Answer:

$\frac{3}{2}, -\frac{4}{3}$