Question

find the solution set.
$6x^2 + 7x + 2 = 0$
separate the two values with a comma.
enter the correct answer.

Explanation:

Step1: Identify quadratic coefficients

For $6x^2 +7x +2=0$, $a=6$, $b=7$, $c=2$

Step2: Apply quadratic formula

Quadratic formula: $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$
Substitute values:
$x=\frac{-7\pm\sqrt{7^2-4\times6\times2}}{2\times6}$

Step3: Calculate discriminant

Compute discriminant:
$\sqrt{49-48}=\sqrt{1}=1$

Step4: Solve for x values

First root:
$x=\frac{-7+1}{12}=\frac{-6}{12}=-\frac{1}{2}$
Second root:
$x=\frac{-7-1}{12}=\frac{-8}{12}=-\frac{2}{3}$

Answer:

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