F(x)=9/x-2

Solution for F(x)=9/x-2 equation:

(F)=9/F-2

We move all terms to the left:

(F)-(9/F-2)=0


Domain of the equation: F-2)!=0

F∈R


We get rid of parentheses

F-9/F+2=0

We multiply all the terms by the denominator


F*F+2*F-9=0

We add all the numbers together, and all the variables

2F+F*F-9=0

Wy multiply elements

F^2+2F-9=0

a = 1; b = 2; c = -9;
Δ = b2-4ac
Δ = 22-4·1·(-9)
Δ = 40
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:

$\sqrt{\Delta}=\sqrt{40}=\sqrt{4*10}=\sqrt{4}*\sqrt{10}=2\sqrt{10}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{10}}{2*1}=\frac{-2-2\sqrt{10}}{2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{10}}{2*1}=\frac{-2+2\sqrt{10}}{2}
$