## Intermediate Algebra: Connecting Concepts through Application

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