F(x)=3x^2+12x+2

Solution for F(x)=3x^2+12x+2 equation:

(F)=3F^2+12F+2

We move all terms to the left:

(F)-(3F^2+12F+2)=0

We get rid of parentheses

-3F^2+F-12F-2=0

We add all the numbers together, and all the variables

-3F^2-11F-2=0

a = -3; b = -11; c = -2;
Δ = b2-4ac
Δ = -112-4·(-3)·(-2)
Δ = 97
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-\sqrt{97}}{2*-3}=\frac{11-\sqrt{97}}{-6}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{97}}{2*-3}=\frac{11+\sqrt{97}}{-6}
$