Question

find the solution set.
6x² + x = 1
separate the two values with a comma.
enter the correct answer.

Explanation:

Step1: Rearrange to standard quadratic form

$6x^2 + x - 1 = 0$

Step2: Apply quadratic formula

For $ax^2+bx+c=0$, $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$. Here $a=6$, $b=1$, $c=-1$:
$$x=\frac{-1\pm\sqrt{1^2-4(6)(-1)}}{2(6)}$$

Step3: Simplify discriminant

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

Step4: Calculate two solutions

$x_1=\frac{-1+5}{12}=\frac{4}{12}=\frac{1}{3}$, $x_2=\frac{-1-5}{12}=\frac{-6}{12}=-\frac{1}{2}$

Answer:

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