3+3/4x=2/x

Solution for 3+3/4x=2/x equation:

3+3/4x=2/x

We move all terms to the left:

3+3/4x-(2/x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

3/4x-(+2/x)+3=0

We get rid of parentheses

3/4x-2/x+3=0

We calculate fractions


3x/4x^2+(-8x)/4x^2+3=0

We multiply all the terms by the denominator


3x+(-8x)+3*4x^2=0

Wy multiply elements

12x^2+3x+(-8x)=0

We get rid of parentheses

12x^2+3x-8x=0

We add all the numbers together, and all the variables

12x^2-5x=0

a = 12; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·12·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5}{2*12}=\frac{0}{24}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*12}=\frac{10}{24}
=5/12
$