Question

$2m^{2}-13m-45=0$
$m=\square$ (use a comma to separate answers as needed.)

Explanation:

Step1: Identify quadratic coefficients

For $2m^2 -13m -45=0$, $a=2$, $b=-13$, $c=-45$

Step2: Apply quadratic formula

$$m=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$$

Step3: Calculate discriminant

$\Delta=(-13)^2-4(2)(-45)=169+360=529$

Step4: Compute square root of discriminant

$\sqrt{529}=23$

Step5: Solve for m values

$m=\frac{13+23}{4}=\frac{36}{4}=9$
$m=\frac{13-23}{4}=\frac{-10}{4}=-\frac{5}{2}$

Answer:

$m = 9, m = -\frac{5}{2}$