(3x-30)/2x=2x/3x

Solution for (3x-30)/2x=2x/3x equation:

(3x-30)/2x=2x/3x

We move all terms to the left:

(3x-30)/2x-(2x/3x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(3x-30)/2x-(+2x/3x)=0

We get rid of parentheses

(3x-30)/2x-2x/3x=0

We calculate fractions


(-4x^2)/6x^2+(9x^2-90x)/6x^2=0

We multiply all the terms by the denominator


(-4x^2)+(9x^2-90x)=0

We get rid of parentheses

-4x^2+9x^2-90x=0

We add all the numbers together, and all the variables

5x^2-90x=0

a = 5; b = -90; c = 0;
Δ = b2-4ac
Δ = -902-4·5·0
Δ = 8100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{8100}=90$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-90}{2*5}=\frac{0}{10}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+90}{2*5}=\frac{180}{10}
=18
$