F(x)=2x/5x-9

Solution for F(x)=2x/5x-9 equation:

(F)=2F/5F-9

We move all terms to the left:

(F)-(2F/5F-9)=0


Domain of the equation: 5F-9)!=0

F∈R


We get rid of parentheses

F-2F/5F+9=0

We multiply all the terms by the denominator


F*5F-2F+9*5F=0

We add all the numbers together, and all the variables

-2F+F*5F+9*5F=0

Wy multiply elements

5F^2-2F+45F=0

We add all the numbers together, and all the variables

5F^2+43F=0

a = 5; b = 43; c = 0;
Δ = b2-4ac
Δ = 432-4·5·0
Δ = 1849
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1849}=43$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(43)-43}{2*5}=\frac{-86}{10}
=-8+3/5
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(43)+43}{2*5}=\frac{0}{10}
=0
$