Question

Solve the equation using quadratic formula.

$4m^2+m-3=0$

Short answer

The solutions are$m=\frac{3}{4},m=1$.

Step-by-step solution

 Given Information.

The given equation is $4m^2+m-3=0$.

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

The quadratic equation is in standard form.

So,

$a=4,b=1,c=-3$

Substitute the values in quadratic formula.

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

$$\begin{gathered} m=\frac{-\left(1\right)\pm \sqrt{(1{)}^2-4(4\left)\right(-3)}}{2\left(4\right)} \\ m=\frac{-1\pm \sqrt{1+48}}{8} \\ m=\frac{-1\pm \sqrt{49}}{8} \\ m=\frac{-1\pm 7}{8} \end{gathered}$$

Rewrite to show two solutions.

$$\begin{gathered} m_1=\frac{-1+7}{8} \\ {m}_1=\frac{3}{4} \\ {m}_2=\frac{-1-7}{8} \\ {m}_2=\frac{-8}{8}=1 \end{gathered}$$

Thus, the solutions are$m=\frac{3}{4},m=1$.