2/5x+4*2/x-1=1

Solution for 2/5x+4*2/x-1=1 equation:

2/5x+4*2/x-1=1

We move all terms to the left:

2/5x+4*2/x-1-(1)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

2/5x+4*2/x-2=0

We calculate fractions


2x/5x^2+200x/5x^2-2=0

We multiply all the terms by the denominator


2x+200x-2*5x^2=0

We add all the numbers together, and all the variables

202x-2*5x^2=0

Wy multiply elements

-10x^2+202x=0

a = -10; b = 202; c = 0;
Δ = b2-4ac
Δ = 2022-4·(-10)·0
Δ = 40804
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{40804}=202$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(202)-202}{2*-10}=\frac{-404}{-20}
=20+1/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(202)+202}{2*-10}=\frac{0}{-20}
=0
$