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

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

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

We move all terms to the left:

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


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

F∈R


We add all the numbers together, and all the variables

F-(-3F+4/F-2)=0

We get rid of parentheses

F+3F-4/F+2=0

We multiply all the terms by the denominator


F*F+3F*F+2*F-4=0

We add all the numbers together, and all the variables

2F+F*F+3F*F-4=0

Wy multiply elements

F^2+3F^2+2F-4=0

We add all the numbers together, and all the variables

4F^2+2F-4=0

a = 4; b = 2; c = -4;
Δ = b2-4ac
Δ = 22-4·4·(-4)
Δ = 68
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{68}=\sqrt{4*17}=\sqrt{4}*\sqrt{17}=2\sqrt{17}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{17}}{2*4}=\frac{-2-2\sqrt{17}}{8}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{17}}{2*4}=\frac{-2+2\sqrt{17}}{8}
$