10/x+(10/2x)=10

Solution for 10/x+(10/2x)=10 equation:

10/x+(10/2x)=10

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

10/x+10/2x-10=0

We calculate fractions


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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

30x-10*2x^2=0

Wy multiply elements

-20x^2+30x=0

a = -20; b = 30; c = 0;
Δ = b2-4ac
Δ = 302-4·(-20)·0
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-30}{2*-20}=\frac{-60}{-40}
=1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+30}{2*-20}=\frac{0}{-40}
=0
$