0,4=x-90/x

Solution for 0,4=x-90/x equation:

0.4=x-90/x

We move all terms to the left:

0.4-(x-90/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-90/x)+0.4=0

We get rid of parentheses

-x+90/x+0.4=0

We multiply all the terms by the denominator


-x*x+(0.4)*x+90=0

We multiply parentheses

-x*x+0.4x+90=0

Wy multiply elements

-1x^2+0.4x+90=0

a = -1; b = 0.4; c = +90;
Δ = b2-4ac
Δ = 0.42-4·(-1)·90
Δ = 360.16
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{360.16}}{2*-1}=\frac{-0.4-\sqrt{360.16}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0.4)+\sqrt{360.16}}{2*-1}=\frac{-0.4+\sqrt{360.16}}{-2}
$