F(-5)=3x-4/x-2

Solution for F(-5)=3x-4/x-2 equation:

(-5)=3F-4/F-2

We move all terms to the left:

(-5)-(3F-4/F-2)=0


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

F∈R


We add all the numbers together, and all the variables

-(3F-4/F-2)-5=0

We get rid of parentheses

-3F+4/F+2-5=0

We multiply all the terms by the denominator


-3F*F+2*F-5*F+4=0

We add all the numbers together, and all the variables

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

Wy multiply elements

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

a = -3; b = -3; c = +4;
Δ = b2-4ac
Δ = -32-4·(-3)·4
Δ = 57
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{-(-3)-\sqrt{57}}{2*-3}=\frac{3-\sqrt{57}}{-6}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{57}}{2*-3}=\frac{3+\sqrt{57}}{-6}
$