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The height of a ball at a given time is modelled by the function h(t)=5t^2+7t+1 where h(t) is in metres and time is in seconds . When will the ball hit the ground

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I think you must mean

h(t) = -5t^2+7t+1

or the ball will never come down at all!

If so, h=0 when t = (7+√69)/10

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