Question

solve for x. write both solutions, separated by a comma.
6x² + x - 1 = 0
enter the correct answer.

Explanation:

Step1: Identify quadratic coefficients

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

Step2: Apply quadratic formula

Quadratic formula: $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$
Substitute values:
$x=\frac{-1\pm\sqrt{1^2-4(6)(-1)}}{2(6)}$

Step3: Calculate discriminant

$\sqrt{1 + 24}=\sqrt{25}=5$

Step4: Compute two solutions

First solution: $x=\frac{-1+5}{12}=\frac{4}{12}=\frac{1}{3}$
Second solution: $x=\frac{-1-5}{12}=\frac{-6}{12}=-\frac{1}{2}$

Answer:

$\frac{1}{3}, -\frac{1}{2}$