F(5)=2x-7/x

Solution for F(5)=2x-7/x equation:

(5)=2F-7/F

We move all terms to the left:

(5)-(2F-7/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

-(+2F-7/F)+5=0

We get rid of parentheses

-2F+7/F+5=0

We multiply all the terms by the denominator


-2F*F+5*F+7=0

We add all the numbers together, and all the variables

5F-2F*F+7=0

Wy multiply elements

-2F^2+5F+7=0

a = -2; b = 5; c = +7;
Δ = b2-4ac
Δ = 52-4·(-2)·7
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-9}{2*-2}=\frac{-14}{-4}
=3+1/2
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+9}{2*-2}=\frac{4}{-4}
=-1
$