x-163/x=0.2

Solution for x-163/x=0.2 equation:

x-163/x=0.2

We move all terms to the left:

x-163/x-(0.2)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

x-163/x-0.2=0

We multiply all the terms by the denominator


x*x-(0.2)*x-163=0

We multiply parentheses

x*x-0.2x-163=0

Wy multiply elements

x^2-0.2x-163=0

a = 1; b = -0.2; c = -163;
Δ = b2-4ac
Δ = -0.22-4·1·(-163)
Δ = 652.04
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{-(-0.2)-\sqrt{652.04}}{2*1}=\frac{0.2-\sqrt{652.04}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.2)+\sqrt{652.04}}{2*1}=\frac{0.2+\sqrt{652.04}}{2}
$