F(x)=6/x+9

Solution for F(x)=6/x+9 equation:

(F)=6/F+9

We move all terms to the left:

(F)-(6/F+9)=0


Domain of the equation: F+9)!=0

F∈R


We get rid of parentheses

F-6/F-9=0

We multiply all the terms by the denominator


F*F-9*F-6=0

We add all the numbers together, and all the variables

-9F+F*F-6=0

Wy multiply elements

F^2-9F-6=0

a = 1; b = -9; c = -6;
Δ = b2-4ac
Δ = -92-4·1·(-6)
Δ = 105
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{-(-9)-\sqrt{105}}{2*1}=\frac{9-\sqrt{105}}{2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{105}}{2*1}=\frac{9+\sqrt{105}}{2}
$