F(2)=3x^2-8x+1

Solution for F(2)=3x^2-8x+1 equation:

(2)=3F^2-8F+1

We move all terms to the left:

(2)-(3F^2-8F+1)=0

We get rid of parentheses

-3F^2+8F-1+2=0

We add all the numbers together, and all the variables

-3F^2+8F+1=0

a = -3; b = 8; c = +1;
Δ = b2-4ac
Δ = 82-4·(-3)·1
Δ = 76
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{76}=\sqrt{4*19}=\sqrt{4}*\sqrt{19}=2\sqrt{19}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{19}}{2*-3}=\frac{-8-2\sqrt{19}}{-6}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{19}}{2*-3}=\frac{-8+2\sqrt{19}}{-6}
$