F(x)=x2+6x+5

Solution for F(x)=x2+6x+5 equation:

(F)=F2+6F+5

We move all terms to the left:

(F)-(F2+6F+5)=0

We add all the numbers together, and all the variables

-(+F^2+6F+5)+F=0

We get rid of parentheses

-F^2-6F+F-5=0

We add all the numbers together, and all the variables

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

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