Question

find the solution set.
$9x^2 + 3x - 2 = 0$
separate the two values with a comma.
enter the correct answer.

Explanation:

Step1: Identify quadratic formula values

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

Step2: Substitute into quadratic formula

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

Step3: Calculate discriminant

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

Step4: Solve for two roots

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

Answer:

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