F(x)=3x/x-5

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

(F)=3F/F-5

We move all terms to the left:

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


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

F∈R


We get rid of parentheses

F-3F/F+5=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

2F+F*F=0

Wy multiply elements

F^2+2F=0

a = 1; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·1·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*1}=\frac{-4}{2}
=-2
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*1}=\frac{0}{2}
=0
$