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+6F+F-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
$