x-1/x=-0.05

Solution for x-1/x=-0.05 equation:

x-1/x=-0.05

We move all terms to the left:

x-1/x-(-0.05)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

x-1/x+0.05=0

We multiply all the terms by the denominator


x*x+(0.05)*x-1=0

We multiply parentheses

x*x+0.05x-1=0

Wy multiply elements

x^2+0.05x-1=0

a = 1; b = 0.05; c = -1;
Δ = b2-4ac
Δ = 0.052-4·1·(-1)
Δ = 4.0025
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{-(0.05)-\sqrt{4.0025}}{2*1}=\frac{-0.05-\sqrt{4.0025}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0.05)+\sqrt{4.0025}}{2*1}=\frac{-0.05+\sqrt{4.0025}}{2}
$