F(x)=4x^2-16x-1

Solution for F(x)=4x^2-16x-1 equation:

(F)=4F^2-16F-1

We move all terms to the left:

(F)-(4F^2-16F-1)=0

We get rid of parentheses

-4F^2+F+16F+1=0

We add all the numbers together, and all the variables

-4F^2+17F+1=0

a = -4; b = 17; c = +1;
Δ = b2-4ac
Δ = 172-4·(-4)·1
Δ = 305
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-\sqrt{305}}{2*-4}=\frac{-17-\sqrt{305}}{-8}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+\sqrt{305}}{2*-4}=\frac{-17+\sqrt{305}}{-8}
$