Question 49728
I think that you have omitted a negative sign from the first term ot the equation: The general form for the function describing the height (as a funtion of time, t) of an object propelled upwards is: {{{h(t) = -16t^2+Vot+Ho}}} where: Vo is the initial upwards velocity and Ho is the initial height.
In your problem, Vo = 112 ft/sec and Ho = 0 (Ground-level), so your equation should be:

{{{h(t) = -16t^2+112t}}} Set h(t) = 180 ft. and solve for t.
{{{180 = -16t^2+112t}}} Subtract 180 from both sides of the equation.
{{{-16t^2+112t-180 = 0}}} Simplify by factoring out a -4.
{{{-4(4t^2-28t+45) = 0}}} 
{{{4t^2-28t+45 = 0}}} Solve by factoring.
{{{(2t-5)(2t-9) = 0}}} Apply the zero product principle.
{{{2t-5 = 0}}} and/or {{{2t-9 = 0}}}
If {{{2t-5 = 0}}} then {{{2t = 5}}} and {{{t = 2.5}}}
If {{{2t-9 = 0}}} then {{{2t = 9}}} and {{{t = 4.5}}}

The arrow reaches a height of 180 ft in 2.5 seconds on its way up and it passes the 180 foot-level on its way down in 4.5 seconds.