Question

In the following exercises, solve by using the Quadratic Formula:$3u^2+7u-2=0$

Short answer

The solution of the equation is$u=-\frac{1}{3};u=-2$

Step-by-step solution

Given information

We are given a quadratic equation is$3u^2+7u-2=0$

Identify the values of a,b,c

On comparing with standard equation we get$a=3,b=7,c=-2$

Write quadratic formula and substitute the values in it

The quadratic formula can be given as

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

On substituting the values we get,

$u=\frac{-7\pm \sqrt{49-4\left(3\right)(-2)}}{2\left(3\right)}$

Simplify

On simplifying we get

$$\begin{gathered} u=\frac{-7\pm \sqrt{49-24}}{6} \\ u=\frac{-7\pm \sqrt{25}}{6} \\ u=\frac{-7\pm 5}{6} \end{gathered}$$

On further simplifying we get

$$\begin{gathered} u=\frac{-7+5}{6} \\ u=\frac{-2}{6} \\ u=\frac{-1}{3} \end{gathered}$$and$$\begin{gathered} u=\frac{-7-5}{6} \\ u=\frac{-12}{6} \\ u=-2 \end{gathered}$$

Conclusion

The solution of the quadratic equation is$q=\frac{1}{3},q=-2$