F(m-2)=4m-5/m

Solution for F(m-2)=4m-5/m equation:

(F-2)=4F-5/F

We move all terms to the left:

(F-2)-(4F-5/F)=0


Domain of the equation: F)!=0

F!=0/1

F!=0

F∈R


We add all the numbers together, and all the variables

(F-2)-(+4F-5/F)=0

We get rid of parentheses

F-4F+5/F-2=0

We multiply all the terms by the denominator


F*F-4F*F-2*F+5=0

We add all the numbers together, and all the variables

-2F+F*F-4F*F+5=0

Wy multiply elements

F^2-4F^2-2F+5=0

We add all the numbers together, and all the variables

-3F^2-2F+5=0

a = -3; b = -2; c = +5;
Δ = b2-4ac
Δ = -22-4·(-3)·5
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-8}{2*-3}=\frac{-6}{-6}
=1
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+8}{2*-3}=\frac{10}{-6}
=-1+2/3
$