Question

Solve the given quadratic equation by using the formula method, $8r^2=r+2$

Answer 1

The given quadratic equation $8r^2=r+2$ which can be rewritten as$8r^2-r-2=0$ is in the form $a{x}^2+bx+c=0$ where $a=8,b=-1$ and $c=-2$.

We know that the quadratic formula is $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

Therefore, substitute $a=8,b=-1$ and $c=-2$ in the formula as follows:

$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}=\frac{-(-1)\pm \sqrt{(-1{)}^2-(4\times 8\times -2)}}{2\times 8}$

$=\frac{1\pm \sqrt{1+64}}{16}$

$=\frac{1\pm \sqrt{65}}{16}$

Hence, $x=\frac{1+\sqrt{65}}{16}$ or $x=\frac{1-\sqrt{65}}{16}$