Question

solve for x. write both solutions, separated by a comma.
$5x^2 + x - 4 = 0$
enter the correct answer.

Explanation:

Step1: Identify quadratic coefficients

For $5x^2 + x - 4 = 0$, we have $a=5$, $b=1$, $c=-4$.

Step2: Apply quadratic formula

The quadratic formula is $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$. Substitute the coefficients:
$$x=\frac{-1\pm\sqrt{1^2-4(5)(-4)}}{2(5)}$$

Step3: Calculate discriminant

Compute the value inside the square root:
$\sqrt{1 + 80}=\sqrt{81}=9$

Step4: Solve for both x values

First solution (using +):
$x=\frac{-1+9}{10}=\frac{8}{10}=\frac{4}{5}$
Second solution (using -):
$x=\frac{-1-9}{10}=\frac{-10}{10}=-1$

Answer:

$-1, \frac{4}{5}$