.4=x-270000/x

Solution for .4=x-270000/x equation:

.4=x-270000/x

We move all terms to the left:

.4-(x-270000/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-270000/x)+.4=0

We add all the numbers together, and all the variables

-(+x-270000/x)+0.4=0

We get rid of parentheses

-x+270000/x+0.4=0

We multiply all the terms by the denominator


-x*x+(0.4)*x+270000=0

We multiply parentheses

-x*x+0.4x+270000=0

Wy multiply elements

-1x^2+0.4x+270000=0

a = -1; b = 0.4; c = +270000;
Δ = b2-4ac
Δ = 0.42-4·(-1)·270000
Δ = 1080000.16
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{-(0.4)-\sqrt{1080000.16}}{2*-1}=\frac{-0.4-\sqrt{1080000.16}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0.4)+\sqrt{1080000.16}}{2*-1}=\frac{-0.4+\sqrt{1080000.16}}{-2}
$