Question

solve for x. write both solutions, separated by a comma.
9x² - 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 roots

First root (using $+$):
$x=\frac{3+9}{18}=\frac{12}{18}=\frac{2}{3}$
Second root (using $-$):
$x=\frac{3-9}{18}=\frac{-6}{18}=-\frac{1}{3}$

Answer:

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