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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-3F^2+9F+1=0

a = -3; b = 9; c = +1;
Δ = b2-4ac
Δ = 92-4·(-3)·1
Δ = 93
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{93}}{2*-3}=\frac{-9-\sqrt{93}}{-6}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{93}}{2*-3}=\frac{-9+\sqrt{93}}{-6}
$