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

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

(3)=3F^2+2F-6

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-3F^2-2F+9=0

a = -3; b = -2; c = +9;
Δ = b2-4ac
Δ = -22-4·(-3)·9
Δ = 112
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-4\sqrt{7}}{2*-3}=\frac{2-4\sqrt{7}}{-6}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+4\sqrt{7}}{2*-3}=\frac{2+4\sqrt{7}}{-6}
$