F(x)=6x^2-2x-3

Solution for F(x)=6x^2-2x-3 equation:

(F)=6F^2-2F-3

We move all terms to the left:

(F)-(6F^2-2F-3)=0

We get rid of parentheses

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

We add all the numbers together, and all the variables

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

a = -6; b = 3; c = +3;
Δ = b2-4ac
Δ = 32-4·(-6)·3
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-9}{2*-6}=\frac{-12}{-12}
=1
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+9}{2*-6}=\frac{6}{-12}
=-1/2
$