Question

Solve the equation using quadratic formula.

$4z^2+2z-6=0$

Short answer

The roots are$z=-\frac{3}{2},z=1$.

Step-by-step solution

 Given Information.     

The given equation is$4z^2+2z-6=0$.

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

$4z^2+2z-6=0$

The equation is in standard form.

So,

$a=4,b=2,c=-6$

Substitute the values in quadratic formula.

$$\begin{gathered} z=\frac{-2\pm \sqrt{(2{)}^2-4(4\left)\right(-6)}}{2\left(4\right)} \\ z=\frac{-2\pm \sqrt{4+96}}{8} \\ z=\frac{-2\pm \sqrt{100}}{8} \end{gathered}$$

Use square root property.  

$z=\frac{-2\pm 10}{8}$

Rewrite to show two solutions.

$$\begin{gathered} z_1=\frac{-2+10}{8} \\ {z}_1=\frac{8}{8} \\ {z}_1=1 \end{gathered}$$

and

$$\begin{gathered} z_2=\frac{-2-10}{8} \\ {z}_2=\frac{-12}{8} \\ {z}_2=\frac{-3}{2} \end{gathered}$$

Thus, the roots are$z=-\frac{3}{2},z=1$.