Question 1202327
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Your post has strange typos. 
I'm assuming it's supposed to be this:
<font color=blue>A ball is thrown from an initial height of 3 feet with an initial upward velocity of 30 ft/s. The ball's height h (in feet) after t seconds is given by the following.
h = 3 + 30t - 16t^2
Find all values of t for which the ball's height is 11 feet.</font>


If my assumption is incorrect, then please let me know.


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We want to find when the ball's height is 11 feet.
We want to find the value(s) of t which lead to h = 11.


{{{h = 3 + 30t - 16t^2}}}


{{{11 = 3 + 30t - 16t^2}}} Replace h with 11.


{{{0 = 3 + 30t - 16t^2-11}}}


{{{0 = -16t^2 + 30t - 8}}}


{{{-16t^2 + 30t - 8 = 0}}}


Then we turn to the quadratic formula.
Plugging in a = -16, b = 30, c = -8
{{{t = (-b +- sqrt(b^2 - 4ac))/(2a)}}}


{{{t = (-30 +- sqrt((30)^2 - 4(-16)(-8)))/(2(-16))}}}


{{{t = (-30 +- sqrt(388))/(-32)}}}


{{{t = (-30 + sqrt(388))/(-32)}}} or {{{t = (-30 - sqrt(388))/(-32)}}}


{{{t = 0.321946}}} or {{{t = 1.553054}}}


Answers: <font color=red>Approximately t = 0.321946 and t = 1.553054</font>
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