Question

In the following exercises, solve by using the Quadratic Formula.$4m^2+m-3=0$

Short answer

The solution of the quadratic equation is $m=-1$and$m=\frac{3}{4}$

Step-by-step solution

Given information

We are given a quadratic equation$4m^2+m-3=0$

Identify the values of a,b,c

On comparing with standard equation we get$a=4,b=1,c=-3$

Write the quadratic formula and substitute the values

The quadratic formula can be given as

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

On substituting the values we get

$m=\frac{-1\pm \sqrt{1-4\left(4\right)(-3)}}{2}$

Simplify

On simplifying we get

$$\begin{gathered} m=\frac{-1\pm \sqrt{1+48}}{8} \\ m=\frac{-1\pm \sqrt{49}}{8} \\ m=\frac{-1\pm 7}{8} \end{gathered}$$

On further simplifying we get

$$\begin{gathered} m=\frac{-1+7}{8} \\ m=\frac{6}{8} \\ m=\frac{3}{4} \end{gathered}$$and$$\begin{gathered} m=\frac{-1-7}{8} \\ m=\frac{-8}{8} \\ m=-1 \end{gathered}$$

Conclusion

The solution of the above equation is $m=-1$and$m=\frac{3}{4}$