F(x)=4x^2-4x-9

Solution for F(x)=4x^2-4x-9 equation:

(F)=4F^2-4F-9

We move all terms to the left:

(F)-(4F^2-4F-9)=0

We get rid of parentheses

-4F^2+F+4F+9=0

We add all the numbers together, and all the variables

-4F^2+5F+9=0

a = -4; b = 5; c = +9;
Δ = b2-4ac
Δ = 52-4·(-4)·9
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-13}{2*-4}=\frac{-18}{-8}
=2+1/4
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+13}{2*-4}=\frac{8}{-8}
=-1
$