Answer
$t = 8, - \frac{7}{3}$
Work Step by Step
$3t^{2} - 17t = 56$
$3t^{2} - 17t - 56 = 0$
$3t^{2} - 24t + 7t - 56 = 0$
$3t(t - 8) + 7(t - 8) = 0$
$(3t + 7)(t-8) = 0$
$t = 8, - \frac{7}{3}$
(Note
$3t + 7 = 0$
$3t = -7$
$t = - \frac{7}{3}$)
Check:
$3(8)^{2} - 17(8) \overset{?}{=} 56$
$3(64) - 136 \overset{?}{=} 56$
$192 - 136 \overset{?}{=} 56$
$56 = 56$
$3( - \frac{7}{3})^{2} - 17( - \frac{7}{3}) \overset{?}{=} 56$
$3(\frac{49}{9}) + \frac{119}{3} \overset{?}{=} 56$
$\frac{49}{3} + \frac{119}{3} \overset{?}{=} 56$
$56 = 56$
