F(x)=2x-1/x+5

Solution for F(x)=2x-1/x+5 equation:

(F)=2F-1/F+5

We move all terms to the left:

(F)-(2F-1/F+5)=0


Domain of the equation: F+5)!=0

F∈R


We get rid of parentheses

F-2F+1/F-5=0

We multiply all the terms by the denominator


F*F-2F*F-5*F+1=0

We add all the numbers together, and all the variables

-5F+F*F-2F*F+1=0

Wy multiply elements

F^2-2F^2-5F+1=0

We add all the numbers together, and all the variables

-1F^2-5F+1=0

a = -1; b = -5; c = +1;
Δ = b2-4ac
Δ = -52-4·(-1)·1
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{-(-5)-\sqrt{29}}{2*-1}=\frac{5-\sqrt{29}}{-2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{29}}{2*-1}=\frac{5+\sqrt{29}}{-2}
$