F(x)=5x/x+1

Solution for F(x)=5x/x+1 equation:

(F)=5F/F+1

We move all terms to the left:

(F)-(5F/F+1)=0


Domain of the equation: F+1)!=0

F∈R


We get rid of parentheses

F-5F/F-1=0

We multiply all the terms by the denominator


F*F-5F-1*F=0

We add all the numbers together, and all the variables

-6F+F*F=0

Wy multiply elements

F^2-6F=0

a = 1; b = -6; c = 0;
Δ = b2-4ac
Δ = -62-4·1·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6}{2*1}=\frac{0}{2}
=0
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6}{2*1}=\frac{12}{2}
=6
$