F(x)+9=-5/x+2

Solution for F(x)+9=-5/x+2 equation:

(F)+9=-5/F+2

We move all terms to the left:

(F)+9-(-5/F+2)=0


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

F∈R


We get rid of parentheses

F+5/F-2+9=0

We multiply all the terms by the denominator


F*F-2*F+9*F+5=0

We add all the numbers together, and all the variables

7F+F*F+5=0

Wy multiply elements

F^2+7F+5=0

a = 1; b = 7; c = +5;
Δ = b2-4ac
Δ = 72-4·1·5
Δ = 29
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{-(7)-\sqrt{29}}{2*1}=\frac{-7-\sqrt{29}}{2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{29}}{2*1}=\frac{-7+\sqrt{29}}{2}
$