Answer
$n = 0.984, -1.544$
Work Step by Step
$2.5n^{2} + 1.4n - 3.8 = 0$
$n = \frac{-(1.4)±\sqrt {(1.4)^{2}-4(2.5)(-3.8)}}{2(2.5)}$
$n = \frac{-1.4±\sqrt {1.96+38}}{5}$
$n = \frac{-1.4±\sqrt {39.96}}{5}$
$n = (0.98427...), (-1.54427...)$
$n = 0.984, -1.544$
Check:
When $n = 0.984$
$2.5(0.984...)^{2} + 1.4(0.984...) - 3.8 \overset{?}{=} 0$
$2.5(0.96880...) + 1.4(0.984...) - 3.8 \overset{?}{=} 0$
$(2.42201...) + (1.3779...) - 3.8 \overset{?}{=} 0$
$(3.7999...) - 3.8 \overset{?}{=} 0$
$3.8 - 3.8 \overset{?}{=} 0$
$0 = 0$
When $n = -1.544$
$2.5(-1.544...)^{2} + 1.4(-1.544...) - 3.8 \overset{?}{=} 0$
$2.5(2.384795...) + (-2.1619...) - 3.8 \overset{?}{=} 0$
$(5.961...) + (-2.1619...) - 3.8 \overset{?}{=} 0$
$3.8- 3.8 \overset{?}{=} 0$
$0 = 0$
