Question

Solve the equation using quadratic formula.

$3m^2+12m+7=0$

Short answer

The roots are$m=\frac{-6+\sqrt{15}}{3},m=\frac{-6-\sqrt{15}}{3}$.

Step-by-step solution

 Given Information.

The given equation is $3m^2+12m+7=0$.

Write the quadratic equation in standard form and identify a,b,c.

$3m^2+12m+7=0$

The equation is in standard form.

So,

$a=3,b=12,c=7$

Substitute the values in quadratic formula.    

$$\begin{gathered} m=\frac{-b\pm \sqrt{b^2-4ac}}{2a} \\ m=\frac{-12\pm \sqrt{(12{)}^2-4(3\left)\right(7)}}{2\left(3\right)} \\ m=\frac{-12\pm \sqrt{144-84}}{6} \\ m=\frac{-12\pm \sqrt{60}}{6} \end{gathered}$$

Use square root property.

$m=\frac{-12\pm 2\sqrt{15}}{6}$

Simplify.

$m=\frac{-6\pm \sqrt{15}}{3}$

Rewrite to show two solutions.

$$\begin{gathered} m=\frac{-6+\sqrt{15}}{3}, \\ m=\frac{-6-\sqrt{15}}{3} \end{gathered}$$