3x/4x=1/x-2

Solution for 3x/4x=1/x-2 equation:

3x/4x=1/x-2

We move all terms to the left:

3x/4x-(1/x-2)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: x-2)!=0

x∈R


We get rid of parentheses

3x/4x-1/x+2=0

We calculate fractions


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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We get rid of parentheses

3x^2+8x^2-4x=0

We add all the numbers together, and all the variables

11x^2-4x=0

a = 11; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·11·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4}{2*11}=\frac{0}{22}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*11}=\frac{8}{22}
=4/11
$