Quadratic and Roots go Hand in Hand

Algebra Level 5

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

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

Give your answer as \( \lfloor c \rfloor \).

Source

Given to me as challenge by me friend Lakshay kumar

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