solve
$\displaystyle \frac{x(15x-1)}{2}=1$
Continuing where dwsmith left off, and multiplying both sides by 2:
$\displaystyle 15x^2-x-2=0$
Factor:
$\displaystyle (5x-2)(3x+1)=0$
Now, by the Zero-product property:
$\displaystyle 5x-2=0$ and $\displaystyle 3x+1=0$
solving gives us:
$\displaystyle x=\frac{2}{5}$
$\displaystyle x=-\frac{1}{3}$