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The graph is a parabola with a minimum point.
So, Substitute the minimum value in the equation y = 3x^2 + 7x + m.
Thus the graph has two x-intercepts the value at the minimum point must be less than 0.
The graph is a parabola with the minimum where x= -b/2a = -7/6.
i.e3(49/36) – 49/6 + m < 0
49/12 – 49/6 + m < 0
(49-98)/12 + m < 0
-49/12 + m < 0
m < 49/12
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