F(x)=3x^2-8x+4

Solution for F(x)=3x^2-8x+4 equation:

(F)=3F^2-8F+4

We move all terms to the left:

(F)-(3F^2-8F+4)=0

We get rid of parentheses

-3F^2+F+8F-4=0

We add all the numbers together, and all the variables

-3F^2+9F-4=0

a = -3; b = 9; c = -4;
Δ = b2-4ac
Δ = 92-4·(-3)·(-4)
Δ = 33
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{-(9)-\sqrt{33}}{2*-3}=\frac{-9-\sqrt{33}}{-6}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{33}}{2*-3}=\frac{-9+\sqrt{33}}{-6}
$