2/x=4/5x+2

Solution for 2/x=4/5x+2 equation:

2/x=4/5x+2

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: 5x+2)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


10x/5x^2+(-4x)/5x^2-2=0

We multiply all the terms by the denominator


10x+(-4x)-2*5x^2=0

Wy multiply elements

-10x^2+10x+(-4x)=0

We get rid of parentheses

-10x^2+10x-4x=0

We add all the numbers together, and all the variables

-10x^2+6x=0

a = -10; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·(-10)·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6}{2*-10}=\frac{-12}{-20}
=3/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*-10}=\frac{0}{-20}
=0
$