F(x)=3(x^2)-12x+6

Solution for F(x)=3(x^2)-12x+6 equation:

(F)=3(F^2)-12F+6

We move all terms to the left:

(F)-(3(F^2)-12F+6)=0

We get rid of parentheses

-3F^2+F+12F-6=0

We add all the numbers together, and all the variables

-3F^2+13F-6=0

a = -3; b = 13; c = -6;
Δ = b2-4ac
Δ = 132-4·(-3)·(-6)
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{-(13)-\sqrt{97}}{2*-3}=\frac{-13-\sqrt{97}}{-6}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+\sqrt{97}}{2*-3}=\frac{-13+\sqrt{97}}{-6}
$