10/x+2=30/2x

Solution for 10/x+2=30/2x equation:

10/x+2=30/2x

We move all terms to the left:

10/x+2-(30/2x)=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-(+30/2x)+2=0

We get rid of parentheses

10/x-30/2x+2=0

We calculate fractions


20x/2x^2+(-30x)/2x^2+2=0

We multiply all the terms by the denominator


20x+(-30x)+2*2x^2=0

Wy multiply elements

4x^2+20x+(-30x)=0

We get rid of parentheses

4x^2+20x-30x=0

We add all the numbers together, and all the variables

4x^2-10x=0

a = 4; b = -10; c = 0;
Δ = b2-4ac
Δ = -102-4·4·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-10}{2*4}=\frac{0}{8}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+10}{2*4}=\frac{20}{8}
=2+1/2
$