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 = 57
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{57}}{2*1}=\frac{9-\sqrt{57}}{2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{57}}{2*1}=\frac{9+\sqrt{57}}{2}
$