F(x)=6x^2-2x-1

Solution for F(x)=6x^2-2x-1 equation:

(F)=6F^2-2F-1

We move all terms to the left:

(F)-(6F^2-2F-1)=0

We get rid of parentheses

-6F^2+F+2F+1=0

We add all the numbers together, and all the variables

-6F^2+3F+1=0

a = -6; b = 3; c = +1;
Δ = b2-4ac
Δ = 32-4·(-6)·1
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{-(3)-\sqrt{33}}{2*-6}=\frac{-3-\sqrt{33}}{-12}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{33}}{2*-6}=\frac{-3+\sqrt{33}}{-12}
$