F(0)=6x^2-9x+3

Solution for F(0)=6x^2-9x+3 equation:

(0)=6F^2-9F+3

We move all terms to the left:

(0)-(6F^2-9F+3)=0

We add all the numbers together, and all the variables

-(6F^2-9F+3)=0

We get rid of parentheses

-6F^2+9F-3=0

a = -6; b = 9; c = -3;
Δ = b2-4ac
Δ = 92-4·(-6)·(-3)
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-3}{2*-6}=\frac{-12}{-12}
=1
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+3}{2*-6}=\frac{-6}{-12}
=1/2
$