10/x+10=12/2x

Solution for 10/x+10=12/2x equation:

10/x+10=12/2x

We move all terms to the left:

10/x+10-(12/2x)=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-(+12/2x)+10=0

We get rid of parentheses

10/x-12/2x+10=0

We calculate fractions


20x/2x^2+(-12x)/2x^2+10=0

We multiply all the terms by the denominator


20x+(-12x)+10*2x^2=0

Wy multiply elements

20x^2+20x+(-12x)=0

We get rid of parentheses

20x^2+20x-12x=0

We add all the numbers together, and all the variables

20x^2+8x=0

a = 20; b = 8; c = 0;
Δ = b2-4ac
Δ = 82-4·20·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8}{2*20}=\frac{-16}{40}
=-2/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8}{2*20}=\frac{0}{40}
=0
$