Question

find the solution set.
7x² - x = 6
separate the two values with a comma.
enter the correct answer.

Explanation:

Step1: Rearrange to standard quadratic form

$7x^2 - x - 6 = 0$

Step2: Apply quadratic formula

For $ax^2+bx+c=0$, $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$. Here $a=7$, $b=-1$, $c=-6$.
$$x=\frac{1\pm\sqrt{(-1)^2-4(7)(-6)}}{2(7)}$$

Step3: Calculate discriminant

$\sqrt{1 + 168}=\sqrt{169}=13$

Step4: Solve for two x values

$x_1=\frac{1+13}{14}=\frac{14}{14}=1$, $x_2=\frac{1-13}{14}=\frac{-12}{14}=-\frac{6}{7}$

Answer:

$1, -\frac{6}{7}$