F(x)=2x-10/x-10

Solution for F(x)=2x-10/x-10 equation:

(F)=2F-10/F-10

We move all terms to the left:

(F)-(2F-10/F-10)=0


Domain of the equation: F-10)!=0

F∈R


We get rid of parentheses

F-2F+10/F+10=0

We multiply all the terms by the denominator


F*F-2F*F+10*F+10=0

We add all the numbers together, and all the variables

10F+F*F-2F*F+10=0

Wy multiply elements

F^2-2F^2+10F+10=0

We add all the numbers together, and all the variables

-1F^2+10F+10=0

a = -1; b = 10; c = +10;
Δ = b2-4ac
Δ = 102-4·(-1)·10
Δ = 140
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:

$\sqrt{\Delta}=\sqrt{140}=\sqrt{4*35}=\sqrt{4}*\sqrt{35}=2\sqrt{35}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{35}}{2*-1}=\frac{-10-2\sqrt{35}}{-2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{35}}{2*-1}=\frac{-10+2\sqrt{35}}{-2}
$