Question

solve for x. write both solutions, separated by a comma.
6x² - 5x - 4 = 0
enter the correct answer.

Explanation:

Step1: Identify quadratic coefficients

For $6x^2 - 5x - 4 = 0$, $a=6$, $b=-5$, $c=-4$

Step2: Apply quadratic formula

Quadratic formula: $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$
Substitute values:
$$x=\frac{-(-5)\pm\sqrt{(-5)^2-4(6)(-4)}}{2(6)}$$

Step3: Calculate discriminant

Compute $\sqrt{25 + 96}=\sqrt{121}=11$
Expression becomes: $x=\frac{5\pm11}{12}$

Step4: Solve for both roots

First root: $x=\frac{5+11}{12}=\frac{16}{12}=\frac{4}{3}$
Second root: $x=\frac{5-11}{12}=\frac{-6}{12}=-\frac{1}{2}$

Answer:

$\frac{4}{3}, -\frac{1}{2}$