F(x)=4x^2-6x-2

Solution for F(x)=4x^2-6x-2 equation:

(F)=4F^2-6F-2

We move all terms to the left:

(F)-(4F^2-6F-2)=0

We get rid of parentheses

-4F^2+F+6F+2=0

We add all the numbers together, and all the variables

-4F^2+7F+2=0

a = -4; b = 7; c = +2;
Δ = b2-4ac
Δ = 72-4·(-4)·2
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{-(7)-9}{2*-4}=\frac{-16}{-8}
=+2
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+9}{2*-4}=\frac{2}{-8}
=-1/4
$