F(x)=3x2-12X+9

Solution for F(x)=3x2-12X+9 equation:

(F)=3F^2-12F+9

We move all terms to the left:

(F)-(3F^2-12F+9)=0

We get rid of parentheses

-3F^2+F+12F-9=0

We add all the numbers together, and all the variables

-3F^2+13F-9=0

a = -3; b = 13; c = -9;
Δ = b2-4ac
Δ = 132-4·(-3)·(-9)
Δ = 61
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{61}}{2*-3}=\frac{-13-\sqrt{61}}{-6}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+\sqrt{61}}{2*-3}=\frac{-13+\sqrt{61}}{-6}
$