Question

solve for x. write both solutions, separated by a comma. 8x² - 2x - 3 = 0 enter the correct answer.

Explanation:

Step1: Identify quadratic coefficients

For $8x^2 - 2x - 3 = 0$, $a=8$, $b=-2$, $c=-3$

Step2: Apply quadratic formula

Quadratic formula: $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$
Substitute values:
$$x=\frac{-(-2)\pm\sqrt{(-2)^2-4(8)(-3)}}{2(8)}$$

Step3: Calculate discriminant

Compute $b^2-4ac$:
$\sqrt{4 + 96}=\sqrt{100}=10$

Step4: Solve for two roots

First root (using $+$):
$x=\frac{2+10}{16}=\frac{12}{16}=\frac{3}{4}$
Second root (using $-$):
$x=\frac{2-10}{16}=\frac{-8}{16}=-\frac{1}{2}$

Answer:

$\frac{3}{4}, -\frac{1}{2}$