20/x+20/2x=10

Solution for 20/x+20/2x=10 equation:

20/x+20/2x=10

We move all terms to the left:

20/x+20/2x-(10)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We calculate fractions


40x/2x^2+20x/2x^2-10=0

We multiply all the terms by the denominator


40x+20x-10*2x^2=0

We add all the numbers together, and all the variables

60x-10*2x^2=0

Wy multiply elements

-20x^2+60x=0

a = -20; b = 60; c = 0;
Δ = b2-4ac
Δ = 602-4·(-20)·0
Δ = 3600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3600}=60$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-60}{2*-20}=\frac{-120}{-40}
=+3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+60}{2*-20}=\frac{0}{-40}
=0
$