What Methods Identify Nonnegative Ranges in Cubic Equations?

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Poster has been reminded to post schoolwor-type questions in the Homework Help forums, and to show some work on the problem
Summary: Cubic equation

How to solve for t ?

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danielp3 said:
( Poster has been reminded to post school work-type questions in the Homework Help forums, and to show some work on the problem. )
Summary: Cubic equation

How to solve for t ?

View attachment 252728
While we wait for you to show some effort at solving this problem, let me make a point.
That is not an equation. That's an inequality.
 
Following on the last hint, suppose the cubic were factored, equivalent to root finding. How would you tell what ranges of t then produced nonnegative values?
 
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