Question

solve for x. write both solutions, separated by a comma.
$4x^2 - x - 3 = 0$
enter the correct answer.

Explanation:

Step1: Identify quadratic coefficients

For $4x^2 - x - 3 = 0$, $a=4$, $b=-1$, $c=-3$

Step2: Apply quadratic formula

Quadratic formula: $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$
Substitute values:
$$x = \frac{-(-1) \pm \sqrt{(-1)^2 - 4(4)(-3)}}{2(4)}$$

Step3: Calculate discriminant

Compute $\sqrt{1 + 48} = \sqrt{49} = 7$
Expression becomes: $x = \frac{1 \pm 7}{8}$

Step4: Solve for two roots

First root: $x = \frac{1 + 7}{8} = \frac{8}{8} = 1$
Second root: $x = \frac{1 - 7}{8} = \frac{-6}{8} = -\frac{3}{4}$

Answer:

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