F(x)=9/x+5

Solution for F(x)=9/x+5 equation:

(F)=9/F+5

We move all terms to the left:

(F)-(9/F+5)=0


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

F∈R


We get rid of parentheses

F-9/F-5=0

We multiply all the terms by the denominator


F*F-5*F-9=0

We add all the numbers together, and all the variables

-5F+F*F-9=0

Wy multiply elements

F^2-5F-9=0

a = 1; b = -5; c = -9;
Δ = b2-4ac
Δ = -52-4·1·(-9)
Δ = 61
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{-(-5)-\sqrt{61}}{2*1}=\frac{5-\sqrt{61}}{2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{61}}{2*1}=\frac{5+\sqrt{61}}{2}
$