F(x)=9/x-8

Solution for F(x)=9/x-8 equation:

(F)=9/F-8

We move all terms to the left:

(F)-(9/F-8)=0


Domain of the equation: F-8)!=0

F∈R


We get rid of parentheses

F-9/F+8=0

We multiply all the terms by the denominator


F*F+8*F-9=0

We add all the numbers together, and all the variables

8F+F*F-9=0

Wy multiply elements

F^2+8F-9=0

a = 1; b = 8; c = -9;
Δ = b2-4ac
Δ = 82-4·1·(-9)
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-10}{2*1}=\frac{-18}{2}
=-9
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+10}{2*1}=\frac{2}{2}
=1
$