F(x)=3x2-4x-2

Solution for F(x)=3x2-4x-2 equation:

(F)=3F^2-4F-2

We move all terms to the left:

(F)-(3F^2-4F-2)=0

We get rid of parentheses

-3F^2+F+4F+2=0

We add all the numbers together, and all the variables

-3F^2+5F+2=0

a = -3; b = 5; c = +2;
Δ = b2-4ac
Δ = 52-4·(-3)·2
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-7}{2*-3}=\frac{-12}{-6}
=+2
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+7}{2*-3}=\frac{2}{-6}
=-1/3
$