Question

find the solution set.
$9x^2 - 3x = 2$
separate the two values with a comma.
enter the correct answer.

Explanation:

Step1: Rewrite to standard quadratic form

$9x^2 - 3x - 2 = 0$

Step2: Identify coefficients for quadratic formula

For $ax^2+bx+c=0$, $a=9$, $b=-3$, $c=-2$

Step3: Apply quadratic formula $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

$$x=\frac{3\pm\sqrt{(-3)^2-4(9)(-2)}}{2(9)}$$

Step4: Calculate discriminant

$\sqrt{9 + 72}=\sqrt{81}=9$

Step5: Solve for two x values

$x_1=\frac{3+9}{18}=\frac{12}{18}=\frac{2}{3}$, $x_2=\frac{3-9}{18}=\frac{-6}{18}=-\frac{1}{3}$

Answer:

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