F(x)=25-5/x

Solution for F(x)=25-5/x equation:

(F)=25-5/F

We move all terms to the left:

(F)-(25-5/F)=0


Domain of the equation: F)!=0

F!=0/1

F!=0

F∈R


We add all the numbers together, and all the variables

F-(-5/F+25)=0

We get rid of parentheses

F+5/F-25=0

We multiply all the terms by the denominator


F*F-25*F+5=0

We add all the numbers together, and all the variables

-25F+F*F+5=0

Wy multiply elements

F^2-25F+5=0

a = 1; b = -25; c = +5;
Δ = b2-4ac
Δ = -252-4·1·5
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*1}=\frac{25-11\sqrt{5}}{2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+11\sqrt{5}}{2*1}=\frac{25+11\sqrt{5}}{2}
$