Question

use the quadratic formula to solve for (x). (8x^{2}+x - 3=0) (if there is more than one solution, separate them with commas)

Explanation:

Step1: Identify coefficients

For the quadratic equation $8x^{2}+x - 3=0$, we have $a = 8$, $b = 1$, $c=-3$.

Step2: Write quadratic formula

The quadratic formula is $x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$.

Step3: Substitute coefficients

Substitute $a = 8$, $b = 1$, $c=-3$ into the formula:
$x=\frac{-1\pm\sqrt{1^{2}-4\times8\times(-3)}}{2\times8}=\frac{-1\pm\sqrt{1 + 96}}{16}=\frac{-1\pm\sqrt{97}}{16}$.

Answer:

$x=\frac{-1+\sqrt{97}}{16},\frac{-1 - \sqrt{97}}{16}$