.2=x-81/x

Solution for .2=x-81/x equation:

.2=x-81/x

We move all terms to the left:

.2-(x-81/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-81/x)+.2=0

We add all the numbers together, and all the variables

-(+x-81/x)+0.2=0

We get rid of parentheses

-x+81/x+0.2=0

We multiply all the terms by the denominator


-x*x+(0.2)*x+81=0

We multiply parentheses

-x*x+0.2x+81=0

Wy multiply elements

-1x^2+0.2x+81=0

a = -1; b = 0.2; c = +81;
Δ = b2-4ac
Δ = 0.22-4·(-1)·81
Δ = 324.04
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{-(0.2)-\sqrt{324.04}}{2*-1}=\frac{-0.2-\sqrt{324.04}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0.2)+\sqrt{324.04}}{2*-1}=\frac{-0.2+\sqrt{324.04}}{-2}
$