Answer
$w=\displaystyle \frac{3}{8}$
Work Step by Step
$ 64w^{2}=48w-9\qquad$...add $-48w+9$ to both sides of the expression.
$ 64w^{2}-48w+9=0\qquad$...recognize a perfect square trinomial.
$(A\pm B)^{2}=A^{2}\pm 2AB+B^{2}$
$(8w-3)^{2}=0$
$(8w-3)(8w-3)=0\qquad$...apply the principle of zero products.
$8w=3$
$w=\displaystyle \frac{3}{8}$
Type the equation into a graphing utility and see
that the graph intercepts the x-axis at $\displaystyle \frac{3}{8}$.
