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^2-1F+1=0

a = -6; b = -1; c = +1;
Δ = b2-4ac
Δ = -12-4·(-6)·1
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-5}{2*-6}=\frac{-4}{-12}
=1/3
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+5}{2*-6}=\frac{6}{-12}
=-1/2
$