F(x)=5/x+4

Solution for F(x)=5/x+4 equation:

(F)=5/F+4

We move all terms to the left:

(F)-(5/F+4)=0


Domain of the equation: F+4)!=0

F∈R


We get rid of parentheses

F-5/F-4=0

We multiply all the terms by the denominator


F*F-4*F-5=0

We add all the numbers together, and all the variables

-4F+F*F-5=0

Wy multiply elements

F^2-4F-5=0

a = 1; b = -4; c = -5;
Δ = b2-4ac
Δ = -42-4·1·(-5)
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-6}{2*1}=\frac{-2}{2}
=-1
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+6}{2*1}=\frac{10}{2}
=5
$