Question

Solve by using the Quadratic Formula:$3m^2+12m+7=0$

Short answer

The solution of the quadratic equation is$m=\frac{-6\pm \sqrt{15}}{3}$

Step-by-step solution

Given information

We are given an equation$3m^2+12m+7=0$

Identify the values of a,b,c

On comparing the equation with standard equation we get$a=3,b=12,c=7$

Write quadratic formula and substitute the values of a,b,c

The quadratic formula can be given as

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

On substituting the values in the formula we get

$m=\frac{-12\pm \sqrt{144-4\left(3\right)\left(7\right)}}{2\left(3\right)}$

Simplify

We get,

$$\begin{gathered} m=\frac{-12\pm \sqrt{144-84}}{6} \\ m=\frac{-12\pm \sqrt{60}}{6} \\ m=\frac{-12\pm 2\sqrt{15}}{6} \end{gathered}$$

Factor out and remove the common factor

We take out and remove the common factor

$$\begin{gathered} m=\frac{2(-6\pm \sqrt{15})}{6} \\ m=\frac{-6\pm \sqrt{15}}{3} \end{gathered}$$

Conclusion

The solution of the quadratic equation is$m=\frac{-6\pm \sqrt{15}}{3}$