Question

solve for x. write both solutions, separated by a comma. 9x² + 6x - 8 = 0 enter the correct answer.

Explanation:

Step1: Identify quadratic coefficients

For $9x^2 + 6x - 8 = 0$, $a=9$, $b=6$, $c=-8$

Step2: Apply quadratic formula

Quadratic formula: $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$
Substitute values:
$$x=\frac{-6\pm\sqrt{6^2-4(9)(-8)}}{2(9)}$$

Step3: Calculate discriminant

Compute $b^2-4ac$:
$\sqrt{36 + 288}=\sqrt{324}=18$

Step4: Solve for both roots

First root (plus sign):
$x=\frac{-6+18}{18}=\frac{12}{18}=\frac{2}{3}$
Second root (minus sign):
$x=\frac{-6-18}{18}=\frac{-24}{18}=-\frac{4}{3}$

Answer:

$\frac{2}{3}, -\frac{4}{3}$