F(x)=x2-4x-1

Solution for F(x)=x2-4x-1 equation:

(F)=F2-4F-1

We move all terms to the left:

(F)-(F2-4F-1)=0

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-1F^2+5F+1=0

a = -1; b = 5; c = +1;
Δ = b2-4ac
Δ = 52-4·(-1)·1
Δ = 29
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{-(5)-\sqrt{29}}{2*-1}=\frac{-5-\sqrt{29}}{-2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{29}}{2*-1}=\frac{-5+\sqrt{29}}{-2}
$