0.15=x-2.23/x

Solution for 0.15=x-2.23/x equation:

0.15=x-2.23/x

We move all terms to the left:

0.15-(x-2.23/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-2.23/x)+0.15=0

We get rid of parentheses

-x+2.23/x+0.15=0

We multiply all the terms by the denominator


-x*x+(0.15)*x+2.23=0

We multiply parentheses

-x*x+0.15x+2.23=0

Wy multiply elements

-1x^2+0.15x+2.23=0

a = -1; b = 0.15; c = +2.23;
Δ = b2-4ac
Δ = 0.152-4·(-1)·2.23
Δ = 8.9425
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{-(0.15)-\sqrt{8.9425}}{2*-1}=\frac{-0.15-\sqrt{8.9425}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0.15)+\sqrt{8.9425}}{2*-1}=\frac{-0.15+\sqrt{8.9425}}{-2}
$