Question

$6m^{2}+11m+4=0$

Explanation:

Step1: Identify quadratic coefficients

For $6m^2+11m+4=0$, $a=6$, $b=11$, $c=4$

Step2: Apply quadratic formula

Quadratic formula: $m=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$
Substitute values:
$$m=\frac{-11\pm\sqrt{11^2-4\times6\times4}}{2\times6}$$

Step3: Calculate discriminant

Compute $b^2-4ac$:
$\sqrt{121-96}=\sqrt{25}=5$

Step4: Solve for m

Substitute discriminant result:
$m=\frac{-11+5}{12}=\frac{-6}{12}=-\frac{1}{2}$
$m=\frac{-11-5}{12}=\frac{-16}{12}=-\frac{4}{3}$

Answer:

$m=-\frac{1}{2}$ or $m=-\frac{4}{3}$