# 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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