Question

solve for x. write both solutions, separated by a comma.
$9x^2 + 3x - 2 = 0$
enter the correct answer.

Explanation:

Step1: Identify quadratic coefficients

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

Step2: Apply quadratic formula

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

Step3: Calculate discriminant

Compute $b^2-4ac$:
$\sqrt{9 + 72} = \sqrt{81} = 9$

Step4: Solve for both x values

First solution:
$x = \frac{-3 + 9}{18} = \frac{6}{18} = \frac{1}{3}$
Second solution:
$x = \frac{-3 - 9}{18} = \frac{-12}{18} = -\frac{2}{3}$

Answer:

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