F(5)=3x^2-8x+2

Solution for F(5)=3x^2-8x+2 equation:

(5)=3F^2-8F+2

We move all terms to the left:

(5)-(3F^2-8F+2)=0

We get rid of parentheses

-3F^2+8F-2+5=0

We add all the numbers together, and all the variables

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

a = -3; b = 8; c = +3;
Δ = b2-4ac
Δ = 82-4·(-3)·3
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-10}{2*-3}=\frac{-18}{-6}
=+3
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+10}{2*-3}=\frac{2}{-6}
=-1/3
$