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

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

(3)=3F^2+F-7

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-3F^2-1F+10=0

a = -3; b = -1; c = +10;
Δ = b2-4ac
Δ = -12-4·(-3)·10
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{-(-1)-11}{2*-3}=\frac{-10}{-6}
=1+2/3
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+11}{2*-3}=\frac{12}{-6}
=-2
$