Answer
$x = \frac{1}{3}, \frac{1}{2}$
Work Step by Step
$6x^{2} = 5x - 1$
$6x^{2} - 5x + 1 = 0$
Find two numbers that will multiply together to get $6$ and can be added together to get $-5$.
$= -2$ and $-3$
$6x^{2} - 3x - 2x + 1 = 0$
$3x(2x - 1) - 1(2x-1) = 0$
$(3x - 1)(2x-1) = 0$
$3x - 1 = 0$
$3x = 1$
$x = \frac{1}{3}$
$2x - 1 = 0$
$2x = 1$
$x = \frac{1}{2}$
$x = \frac{1}{3}, \frac{1}{2}$