Question

Solve the equation using quadratic formula.

$3u^2+7u-2=0$

Short answer

The roots are$u=\frac{-7+\sqrt{73}}{6},u=\frac{-7-\sqrt{73}}{6}$.

Step-by-step solution

 Given Information.  

The given equation is$3u^2+7u-2=0$.

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

The quadratic equation is in standard form.

So,

$a=3,b=7,c=-2$

Substitute the values in quadratic formula. 

$$\begin{gathered} u=\frac{-b\pm \sqrt{b^2-4ac}}{2a} \\ u=\frac{-7\pm \sqrt{7^2-4\left(3\right)(-2)}}{2\left(3\right)} \\ u=\frac{-7\pm \sqrt{49+24}}{6} \\ u=\frac{-7\pm \sqrt{73}}{6} \end{gathered}$$

Rewrite to show two solutions.  

$$\begin{gathered} u=\frac{-7+\sqrt{73}}{6} \\ u=\frac{-7-\sqrt{73}}{6} \end{gathered}$$

Thus, the solutions are$u=\frac{-7\pm \sqrt{73}}{6}$.