F(6)=3x^2-7x

Solution for F(6)=3x^2-7x equation:

(6)=3F^2-7F

We move all terms to the left:

(6)-(3F^2-7F)=0

We get rid of parentheses

-3F^2+7F+6=0

a = -3; b = 7; c = +6;
Δ = b2-4ac
Δ = 72-4·(-3)·6
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-11}{2*-3}=\frac{-18}{-6}
=+3
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+11}{2*-3}=\frac{4}{-6}
=-2/3
$