F(x)=5-1/5x

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

(F)=5-1/5F

We move all terms to the left:

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


Domain of the equation: 5F)!=0

F!=0/1

F!=0

F∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

F+1/5F-5=0

We multiply all the terms by the denominator


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

Wy multiply elements

5F^2-25F+1=0

a = 5; b = -25; c = +1;
Δ = b2-4ac
Δ = -252-4·5·1
Δ = 605
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:

$\sqrt{\Delta}=\sqrt{605}=\sqrt{121*5}=\sqrt{121}*\sqrt{5}=11\sqrt{5}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-11\sqrt{5}}{2*5}=\frac{25-11\sqrt{5}}{10}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+11\sqrt{5}}{2*5}=\frac{25+11\sqrt{5}}{10}
$