Question

select the value(s) of x that make the following equation true
$6x^2 - 13x = -5$
$\square\\ x = -5$
$\square\\ x = \frac{5}{4}$
$\square\\ x = \frac{4}{3}$
$\square\\ x = \frac{1}{2}$
$\square\\ x = \frac{5}{3}$

Explanation:

Step1: Rewrite to standard quadratic form

$6x^2 - 13x + 5 = 0$

Step2: Factor the quadratic equation

$(2x - 1)(3x - 5) = 0$

Step3: Solve for each factor

Set $2x - 1 = 0$: $x = \frac{1}{2}$
Set $3x - 5 = 0$: $x = \frac{5}{3}$

Step4: Verify options

Check which given options match the solutions.

Answer:

$x = \frac{1}{2}$, $x = \frac{5}{3}$