Answer
$w\approx5.93$, $w\approx2.07$
Work Step by Step
$33=-7(4-w)^2+59$
$-7(4-w)^2+59=33$
$-7(4-w)^2=33-59$
$-7(4-w)^2=-26$
$7(4-w)^2=26$
$7(4^2+w^2-8w)=26$
$7(16+w^2-8w)=26$
$112+7w^2-56w-26=0$
$7w^2-56w+86=0$
$aw^2+bw+c=0$
$a=7,b=-56,c=86$
$w=\frac{56 \pm \sqrt {(-56)^2-4\times7\times86}}{2\times7}$
$w=\frac{56 \pm 2\sqrt {182}}{2\times7}$
$w=2[\frac{28 \pm \sqrt {182}}{2\times7}]$
$w=\frac{28 \pm \sqrt {182}}{7}$
$w\approx5.93$, $w\approx2.07$