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Try correct the given 2h^2-5h-12>=0;

by factoring;

h=-3/2 ; h=4;
pre plot:             ----------o------O---------------o---
                                     -3/2                          4;
lets do it in a table;

Inequality                2h+3(h-4)           >=0;
h<-3/2                        (-)  (-)=+>0     satisfy the inequality;
-3/2<h<4                    (+) (-)=->0      does not satisfy;
h>4                             (+) (+)=+>0    satisfy the ineq;

solution set: {h/(h<=-3/2, h>=4)] this is a closed interval;
re plot:

  h          -3/2                                 4   h;

* means closed interval

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