F(x)=3x2-6x+2

Solution for F(x)=3x2-6x+2 equation:

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-3F^2+7F-2=0

a = -3; b = 7; c = -2;
Δ = b2-4ac
Δ = 72-4·(-3)·(-2)
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-5}{2*-3}=\frac{-12}{-6}
=+2
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+5}{2*-3}=\frac{-2}{-6}
=1/3
$