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:

$$ x=\frac{-6\pm\sqrt{6^2-4\times9\times(-8)}}{2\times9} $$

Step3: Calculate discriminant

Compute $b^2-4ac$:

$$ 6^2-4\times9\times(-8)=36+288=324 $$

Step4: Simplify square root

$\sqrt{324}=18$

Step5: Solve for two x values

First solution (plus sign):

$$ x=\frac{-6+18}{18}=\frac{12}{18}=\frac{2}{3} $$

Second solution (minus sign):

$$ x=\frac{-6-18}{18}=\frac{-24}{18}=-\frac{4}{3} $$

Answer:

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