0.9=x-1/x

Solution for 0.9=x-1/x equation:

0.9=x-1/x

We move all terms to the left:

0.9-(x-1/x)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-(+x-1/x)+0.9=0

We get rid of parentheses

-x+1/x+0.9=0

We multiply all the terms by the denominator


-x*x+(0.9)*x+1=0

We multiply parentheses

-x*x+0.9x+1=0

Wy multiply elements

-1x^2+0.9x+1=0

a = -1; b = 0.9; c = +1;
Δ = b2-4ac
Δ = 0.92-4·(-1)·1
Δ = 4.81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0.9)-\sqrt{4.81}}{2*-1}=\frac{-0.9-\sqrt{4.81}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0.9)+\sqrt{4.81}}{2*-1}=\frac{-0.9+\sqrt{4.81}}{-2}
$