Question

find the solution set.
9x² + 5x = 4
separate the two values with a comma.
enter the correct answer.

Explanation:

Step1: Rearrange to standard quadratic form

$9x^2 + 5x - 4 = 0$

Step2: Apply quadratic formula

For $ax^2+bx+c=0$, $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$. Here $a=9$, $b=5$, $c=-4$.
$$x=\frac{-5\pm\sqrt{5^2-4(9)(-4)}}{2(9)}$$

Step3: Calculate discriminant

$\sqrt{25 + 144}=\sqrt{169}=13$

Step4: Compute two solutions

$x_1=\frac{-5+13}{18}=\frac{8}{18}=\frac{4}{9}$
$x_2=\frac{-5-13}{18}=\frac{-18}{18}=-1$

Answer:

$-1, \frac{4}{9}$