Question

In the following exercises, solve by using the Quadratic Formula.

$6x^2+2x-20=0$

Short answer

The solutions of the given equation are $x=\frac{5}{3}$and $x=-2$.

Step-by-step solution

Step 1. Given information.

The given equation is:

$6x^2+2x-20=0$

Step 2. Substitute the values in Quadratic Formula.

Quadratic Formula for the equation $a{x}^2+bx+c=0$is:

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

In the given equation, $a=6,b=2,c=-20$. Substitute these values in Quadratic Formula.

$x=\frac{-2\pm \sqrt{2^2-4\left(6\right)(-20)}}{2\left(6\right)}$

Step 3. Simplify the value.

On simplification, we get

$\begin{array}{rcl}x& =& \frac{-2\pm \sqrt{4+480}}{12}\\ x& =& \frac{-2\pm \sqrt{484}}{12}\\ x& =& \frac{-2\pm 22}{12}\end{array}$

It can be written as:

$$\begin{gathered} x=\frac{-2+22}{12}\text{and}x=\frac{-2-22}{12} \\ x=\frac{20}{12}\text{and}x=\frac{-24}{12} \\ x=\frac{5}{3}\text{and}x=-2 \end{gathered}$$

Step 4. Conclusion.

The solutions of the given equation are $x=\frac{5}{3}$and $x=-2$.