Question

Solve the equation using quadratic formula.

$5q^2-11q+3=0$

Short answer

The roots are$q=\frac{11+\sqrt{61}}{10},q=\frac{11-\sqrt{61}}{10}$.

Step-by-step solution

 Given Information.    

The given equation is$5q^2-11q+3=0$.

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

$5q^2-11q+3=0$

The equation is in standard form.

So,

$a=5,b=-11,c=3$

Substitute the values in quadratic formula. 

$$\begin{gathered} q=\frac{-b\pm \sqrt{b^2-4ac}}{2a} \\ q=\frac{-(-11)\pm \sqrt{(-11{)}^2-4(5\left)\right(3)}}{2\left(5\right)} \\ q=\frac{11\pm \sqrt{121-60}}{10} \\ q=\frac{11\pm \sqrt{61}}{10} \end{gathered}$$

Rewrite to show two solutions.

$$\begin{gathered} q=\frac{11+\sqrt{61}}{10}, \\ q=\frac{11-\sqrt{61}}{10} \end{gathered}$$

Thus, the roots are$q=\frac{11+\sqrt{61}}{10},q=\frac{11-\sqrt{61}}{10}$.