Answer
$\displaystyle \{-\frac{3}{4},\frac{5}{6}\}$
Work Step by Step
...subtract 15
$24x^{2}-2x-15=0$
... factoring, we seek factors of $ac=-360$ whose sum is $b=-2$
... we find +18 and -20
$24x^{2}-20x+18x-15=0$
$4x(6x-5)+3(6x-5)=0$
$(6x-5)(4x+3)=0$
$6x-5=0\displaystyle \quad\Rightarrow\quad x=\frac{5}{6}$
$4x+3=0\displaystyle \quad\Rightarrow\quad x=-\frac{3}{4}$
Solution set = $\displaystyle \{-\frac{3}{4},\frac{5}{6}\}$
