x-13/x=0.55

Solution for x-13/x=0.55 equation:

x-13/x=0.55

We move all terms to the left:

x-13/x-(0.55)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

x-13/x-0.55=0

We multiply all the terms by the denominator


x*x-(0.55)*x-13=0

We multiply parentheses

x*x-0.55x-13=0

Wy multiply elements

x^2-0.55x-13=0

a = 1; b = -0.55; c = -13;
Δ = b2-4ac
Δ = -0.552-4·1·(-13)
Δ = 52.3025
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{-(-0.55)-\sqrt{52.3025}}{2*1}=\frac{0.55-\sqrt{52.3025}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.55)+\sqrt{52.3025}}{2*1}=\frac{0.55+\sqrt{52.3025}}{2}
$