F(x)=2x/x-7

Solution for F(x)=2x/x-7 equation:

(F)=2F/F-7

We move all terms to the left:

(F)-(2F/F-7)=0


Domain of the equation: F-7)!=0

F∈R


We get rid of parentheses

F-2F/F+7=0

We multiply all the terms by the denominator


F*F-2F+7*F=0

We add all the numbers together, and all the variables

5F+F*F=0

Wy multiply elements

F^2+5F=0

a = 1; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·1·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*1}=\frac{-10}{2}
=-5
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*1}=\frac{0}{2}
=0
$