Quadratic and Roots go Hand in Hand

Algebra Level 5

Let f(x)=3x27x+c f\left( x \right) =3{ x }^{ 2 }-7x+c where cc is variable cofficient with x>76 x > \frac 7 6.

Determine the value of cc such that f(x) f\left( x \right) touches g(x)=12x+4912c+76 g\left( x \right) =\frac { \sqrt { 12x+49-12c } +7 }{ 6 }

Give your answer as c \lfloor c \rfloor .

Source

Given to me as challenge by me friend Lakshay kumar

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