x-2.23/x=0.15

Solution for x-2.23/x=0.15 equation:

x-2.23/x=0.15

We move all terms to the left:

x-2.23/x-(0.15)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

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

x^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}
$