Answer
$30$ mi/h.
Work Step by Step
We are given:
$d=x+ \frac{x^{2}}{20}$
We know that $d=75$ and must find the speed $x$:
$75=x+ \frac{x^{2}}{20}$
$75*20=20x+ x^{2}$
$1500=20x+x^{2}$
$x^{2}+20x-1500=0$
$(x-30)(x+50)=0$
$x-30=0$ or $x+50=0$
$x=30$ or $x=-50$
Since the speed can't be negative, we use the left solution. So the speed must have been $30$ mi/h.
