F(x)=x/5x+8

Solution for F(x)=x/5x+8 equation:

(F)=F/5F+8

We move all terms to the left:

(F)-(F/5F+8)=0


Domain of the equation: 5F+8)!=0

F∈R


We get rid of parentheses

F-F/5F-8=0

We multiply all the terms by the denominator


F*5F-F-8*5F=0

We add all the numbers together, and all the variables

-1F+F*5F-8*5F=0

Wy multiply elements

5F^2-1F-40F=0

We add all the numbers together, and all the variables

5F^2-41F=0

a = 5; b = -41; c = 0;
Δ = b2-4ac
Δ = -412-4·5·0
Δ = 1681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1681}=41$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-41)-41}{2*5}=\frac{0}{10}
=0
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-41)+41}{2*5}=\frac{82}{10}
=8+1/5
$