F(x)=x^2+5x-1

Solution for F(x)=x^2+5x-1 equation:

(F)=F^2+5F-1

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

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

a = -1; b = -4; c = +1;
Δ = b2-4ac
Δ = -42-4·(-1)·1
Δ = 20
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{20}=\sqrt{4*5}=\sqrt{4}*\sqrt{5}=2\sqrt{5}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{5}}{2*-1}=\frac{4-2\sqrt{5}}{-2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{5}}{2*-1}=\frac{4+2\sqrt{5}}{-2}
$