F(x)=1/x+25

Solution for F(x)=1/x+25 equation:

(F)=1/F+25

We move all terms to the left:

(F)-(1/F+25)=0


Domain of the equation: F+25)!=0

F∈R


We get rid of parentheses

F-1/F-25=0

We multiply all the terms by the denominator


F*F-25*F-1=0

We add all the numbers together, and all the variables

-25F+F*F-1=0

Wy multiply elements

F^2-25F-1=0

a = 1; b = -25; c = -1;
Δ = b2-4ac
Δ = -252-4·1·(-1)
Δ = 629
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{-(-25)-\sqrt{629}}{2*1}=\frac{25-\sqrt{629}}{2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+\sqrt{629}}{2*1}=\frac{25+\sqrt{629}}{2}
$