1/0,5x+2/x=3

Solution for 1/0,5x+2/x=3 equation:

1/0.5x+2/x=3

We move all terms to the left:

1/0.5x+2/x-(3)=0


Domain of the equation: 0.5x!=0

x!=0/0.5

x!=0

x∈R



Domain of the equation: x!=0

x∈R


We calculate fractions


x/(0.5x*x)+x/(0.5x*x)-3=0

We add all the numbers together, and all the variables

x/(+0.5x*x)+x/(+0.5x*x)-3=0

We multiply all the terms by the denominator


x+x-3*(+0.5x*x)=0

We add all the numbers together, and all the variables

2x-3*(+0.5x*x)=0

We multiply parentheses

-0x^2+2x=0

We add all the numbers together, and all the variables

-1x^2+2x=0

a = -1; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·(-1)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*-1}=\frac{-4}{-2}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*-1}=\frac{0}{-2}
=0
$