x-5/x=0.4

Solution for x-5/x=0.4 equation:

x-5/x=0.4

We move all terms to the left:

x-5/x-(0.4)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

x-5/x-0.4=0

We multiply all the terms by the denominator


x*x-(0.4)*x-5=0

We multiply parentheses

x*x-0.4x-5=0

Wy multiply elements

x^2-0.4x-5=0

a = 1; b = -0.4; c = -5;
Δ = b2-4ac
Δ = -0.42-4·1·(-5)
Δ = 20.16
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{-(-0.4)-\sqrt{20.16}}{2*1}=\frac{0.4-\sqrt{20.16}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.4)+\sqrt{20.16}}{2*1}=\frac{0.4+\sqrt{20.16}}{2}
$